The lens' aperture diameter (entrance pupil) determines how much light passes through the lens, and the lens' magnification (focal length) determines how spread out that light is; those two factors combine as the f#. Aperture (f#) alone determines the intensity/density (luminous flux) of the light at the image plane.
SS then determines for how long the image plane is illuminated with that intensity, and ISO adjusts the output brightness of the resulting exposure... exposure is size/area independent.
In your big window/little window analogy, the correct "window" is the size of the image plane/sensor, not the size of the pixels "behind" it. In your house you can stand behind a large window or a small window and it will make no difference; if you place your hand (small pixel) in the opening, or your face (larger pixel) in the opening, both will receive the same illumination (exposure/area); and that's *all that matters. But a larger window does pass more light overall; and similarly a larger image area/sensor receives more light as well. That last bit is often confused as "larger pixels" when discussing different sized sensors of the same resolution; but that is the wrong correlation.
DP review has a **good comparison tool. This is set for four Nikon cameras, low light, and the same output size. The top row is the 16MP D4 (7.3um) and the 46MP D850 (4.3um), both are FF sensors. The bottom row is of two smaller sensors.
The D4 image is a little out of focus which helps it a bit, but otherwise the noise in the top row is nearly the same (it will never be identical because it is random). The 1.5x crop factor D7500 image is noticeably noisier even though its' pixels are the same size as the D850 (4.2um); and the 2.7x V3 is much worse.
*at the extremes there can be notable differences in fill efficiencies that would make the larger pixels more effective; but that is essentially a non-factor in any realistic comparison.
** The comparisons reduce the exposure by changing the SS, so the ISO noise results may differ from reduced exposure due to lower light levels.