You are probably missing some points.
HDR first of all is a concept, having more dynamic range.
Second, is about the ammount of information. A real HDRI file has a floating point information, that is an optimized way to store huge diference in values. It is more effieient than defining for example 16 million possible values.
But we need to transform that "RAW" information into a more usable one. This is what tonnal map does. 16 bit image has plenty room to adjust and play a visible and reproducable image.
RAW is not a file type by itself, it is a type of unprocessed information.
A TIF file can store diferent deepth of pixel information that can be readed by diferent programs Normally an usable tiff file can store 8 or 16 bits per channel (24, 32, 48 total bits).
32 bits per channel is several billions of levels, so it is quite complex to handle. (Do not confuse this to 32 bits total, which is a CMYK image)
But if you work in photoshop the best option is to use the native file format. PSD.
A normal monitor displays only 256 levels of each color, 8 bit, potentially displaying 16 million diferent shades. (24 bit images)
Some monitors have a hughe contrast, for example 10000:1, but this is how diferent the shade 0 is from the shade 256. This not mean that displays 10,000 diferent tones, it is how separated the tones are.
Some monitors mark the display as 32 bit, instead of 24. This is in reality used by the Operating system to indicate it can handle transparent objects rendered, for example a transparent window when you move it. This 3d are not per channel, are 8 bit for each RGB channel (24, plus transparency 24+8=32).
You can not "scale down" a bit depth, you simply reduce it.
But again, do not confuse X bit images to X bit per channel
I can change my monitor from 16 to 32bit
This is total bit depth, not per channel. a 16 bit monitor is total bits, so it can only display 65,000 diferent colors, so you will see banding. Leave your monitor to 24 or 32 bits.