First off, let's understand what a "raw photo" is and, perhaps more importantly, what it is not. You'll never see "THE raw image" on your camera's rear LCD and probably never on your computer's monitor. An "unprocessed" raw image file would be almost unrecognizable.
Raw image files contain enough data to create a near infinite number of interpretations of that data that will fit in an 8-bit jpeg file. Anytime you open a raw file and look at it on your screen, you are not viewing "THE raw file." You are viewing one among countless possible interpretations of the data in the raw file converted to a JPEG-like image that your monitor is capable of displaying. The raw data itself contains a single (monochrome) brightness value measured by each photosite (a/k/a pixel well or sensel). With Bayer masked camera sensors (the vast majority of color digital cameras use Bayer filters) each photosite has a color filter in front of it that is either red, green, or blue.¹ For a more complete discussion of how we get color information out of the single brightness values measured at each pixel well, please see RAW files store 3 colors per pixel, or only one?
¹ The actual colors of the Bayer mask in front of the sensors of most color digital cameras are: Blue - a slightly violet version of blue centered at 450 nanometers, Green - a slightly yellowish version of green centered on about 535-540 nanometers, and Red - a slightly orange version of yellow. What we call "red" is the color we perceive for light at about 640 nanometers in wavelength. The "red" filters on most Bayer arrays allow the most light through at somewhere around 590-600 nanometers. The overlap between the "green" and "red" cones in the human retina are even closer than that, with "red" centered at about 565 nanometers, which is what we perceive as lime green.
A raw data file has no implicit color. The application that you use to open that file will either use its own default color conversion settings to display the image, or it may use another set of instructions you've told it to use by default. Initially, it may display the preview JPEG image that is attached to the raw file by your camera. The JPEG preview will be created using the settings in your camera at the time you took the photo. If some of your in-camera settings at the time for things such as contrast, color temperature, and white balance were "Auto", then the engineers who wrote your cameras firmware will have determined what white balance will be applied to the JPEG preview based on what the camera's image processor reads from the monochromatic luminance values in the raw file.
White balance settings affect how the monochrome luminance values recorded by the sensor are demosaiced (a/k/a de-Bayered) and the color multipliers used for each channel before response curves are applied in order to transform the linear response of digital sensors to the logarithmic response of the human eye/brain visual system. The way demosaicing works is amazingly similar to how our eye/brain system works to create a perception of color from the stimulation of our retinal cones due to various combinations of wavelengths of the portion of the electromagnetic spectrum that we call visible light.
Another thing it is vital for us to understand is that color is strictly a product of perception. Wavelengths of light do not have implicit color. For humans, color is created by our brain as it interprets the signals it receives from our retinal cones. There is no fundamental difference between what we call "visible light" and other portions of the electromagnetic spectrum. We call it visible light because our human retinal cones have a biochemical response to that portion of the electromagnetic spectrum while at the same time we do not have a biochemical response to X-rays, radio waves, etc. that are other parts of the electromagnetic spectrum with shorter or longer wavelengths than the visible light portion of it. When we say something like "spectral red is the color of light at a wavelength of 640 nanometers" what we really mean is that red is the color humans perceive when their retinal cones are stimulated by electromagnetic radiation at 640 nm. This perception of "red" is the result of the different response intensity generated by our short wavelength cones that are most sensitive to around 420nm (blue-violet), our medium wavelength cones that are most sensitive to around 534nm (slightly yellowish green), and our long wavelength cones that are most sensitive to around 564nm (lime-green). The lack of much of any response by the S cones, a moderate response by the M cones, and a slightly more elevated response by the L cones causes our human brains to create a perception of "red". Almost all of the colors humans perceive can not be stimulated by a single wavelength, but require multiple wavelengths of light mixed in various ratios to stimulate the perception of a specific color.
Other species may or may not even have a biochemical response at all to light at 640nm. If they do not, then when they are exposed to 640nm electromagnetic radiation they do not see red. They do not see anything, just as we do not see anything when exposed to 900nm infrared light, 176m (1.76 x 10^11 nm) AM radio waves, 100-350nm UV, or 3nm X-rays.
When raw digital image data is being processed, it's done in a sequence of steps. The first steps must necessarily be done before the next steps can be applied. You can't, for example, apply HSL adjustments or RGB tone curves to the monochrome luminance values recorded in a raw image file until after you've demosaiced that monochrome information into color information. The application must transform those luminance values into color information before specific adjustments of certain specific colors can be made.
White balance is determined by a combination of a value along the amber ←→ blue color temperature axis and a tint value along the green ←→ magenta axis. They are roughly orthogonal to each other. When we set the white balance we tell the application we are using that the light illuminating our photograph was centered on this point in CIE color space. Any area of the scene we photographed that returns these same ratios of amber ←→ blue and magenta ←→ green should be rendered as a neutral gray tone somwhere between black and white.
The color temperature axis within a portion of CIE color space. Notice that common white balance settings such as D50 and D65 are in a slightly green direction from the color temperature axis.
White balance is the first thing that is applied when the single luminance values recorded by each photosite on the surface of the camera's sensor are demosaiced. The R, G, and B values of every pixel in the digital image are interpolated by comparing the relative brightnesses of the single luminance values recorded by adjoining and nearby photosites filtered with each of the three colors used by the Bayer mask (or other type of color filter array).
The color filters in front of each photosite do not transform that single luminance value to a specific color because those filters do not reject all light not that specific color to pass. They're much like the color filters we use when doing black and white film photography. Some of all of the colors still pass through, for example, a deep red filter. But much less of the shorter wavelength blue light falling on it is allowed to pass than the longer wavelength red light falling on it. Thus objects that are deep blue, such as a cloudless sky in late afternoon, will show up in a B&W image as darker than would have been the case without the deep red filter. Red objects, on the other hand, show up just as bright in the B&W image both with and without the filter. Wavelengths between the two ends of the visible spectrum are reduced, but they are reduced by less than the shorter bluer ones. If we increase exposure to account for the total light loss of the filter, red objects (and objects, such as white snow or light grey stone, that include a lot of red within the wavelengths those objects are reflecting) will actually appear brighter in the filtered shot than in the non-filtered shot.
Two consecutive exposures of Half Dome in the Yosemite Valley made by Ansel Adams in 1927. He titled the left one, taken after he realized the right one would not give him the contrast he desired between the sky and rock face, "Monolith'. The photo on the left used a strong Wratten #29 deep red filter, the one on the right used a weak K2 Yellow filter that Adams often used. There was very little, if any "red" in the scene. The effect of the red filter was to attenuate some wavelengths of light (specifically those on the blue end of the visible spectrum) more than others. This was a pivotal moment in the life of Adams when he first realized he could visualize the photograph he wanted to produce before he exposed the negative and take steps at the point of exposure to alter how the negative was exposed in order to get the result he wanted.
The brightness values recorded by each photosite behind each of the three types of color filters can also not be correctly transformed into an R, G, or B value without transformation because the colors used by the filters and the colors used by our RGB emissive displays are not the same three colors.
Once demosaicing and color channel multipliers based on the current white balance setting have been applied to the data from a digital camera, the image contains RGB values for each pixel in the image.
If one uses the Tone Curve adjustment in Lightroom, for example, one can adjust the relative tones of all three color channels or one can adjust the values of each of the three color channels independently of the other two. Of course lowering the value of one of the three channels makes the other two channels look stronger. Raising the value of one channel lessens the influence of the other two on the color that we will perceive for each affected pixel.
Our processing/editing applications can also divide the millions of different possible colors (that is, the millions of possible combinations of R, G, and B values for each pixel in the image) into what may be visualized as slices of pie around a color wheel. Various combinations of hue will be placed in each of the pie slices. When we use an HSL/HSB/HSV tool, the changes we make apply to only one slice of that pie.
Even within a specific hue, values that are very bright (visualize these pixels as occupying space above the pie's top crust) or very dark (visualize these pixels as occupying space below the pie's lower crust), and thus also less saturated as they approach either pure white or pure black, will not be affected by HSL adjustments to the same extent that the same hue with more medium brightness values will. Some of our applications even allow us to make the portion of the pie that our adjustments affect slimmer (affecting fewer colors more closely adjacent to our target color) or wider (affecting more of the colors more widely adjacent to our target color).
At this point if we then go back and change the white balance settings we're not really "shifting" anything we see on the screen at that point. We're telling the app to go back to the monochromatic luminance values it started with and demosaic all over again using different color multipliers. Once the app does that, it will then reapply any subsequent instructions we've included in the processing pipeline, such as tone curve adjustments or HSL adjustments. But those subsequent instructions will only be applied to the newer results of the most recent demosaicing instructions using the current white balance setting.
Some, many, or even all of the pixels which once fell in one slice of the color wheel pie with the old white balance setting will now fall in a different slice with the new white balance setting. Thus whatever adjustment have been made in the HSL/HSB/HSV tool will not necessarily apply to the same pixels they did before. They'll only apply to the pixels that fall in that slice of the color wheel pie after the raw data has been demosaiced again with the new white balance settings.
In your theoretical example the lake appears blue with your initial color temperature setting of, say, 5200K. If you've used your HSL tool to increase saturation of blue and decrease the luminance of blue your lake will look more intensely blue while also being darker than before the HSL adjustment. You then go back and change the color temperature to 10000K (50000K is a bit extreme, as you'd only come out with a pretty much totally monochromatic image with every pixel the same or very similar hue and only the brightness values of each pixel being higher or lower than other pixels.) Now the same pixels that made the lake look blue are an orange-red color. The adjustment of the blue portion in your HSL tool is no longer applied to those pixels because after the new demosaicing setting those pixels no longer fall within the range of the blue adjustment. To affect those pixels with your HSL tool you'll need to move the sliders in the orange and red portions of the HSL tool.