That's not right. Most monitors use 8 bits per color / 24 bits per pixel, though some are still using 6 bpc / 18bpp.
HDR doesn't mean or really require more than 8bpc, it's more complicated than that. To skip all the complicated details, it means more brightness, more contrast and better colors, and it makes a big difference for OLED displays especially.
Sounds like you want color management, not just arbitrary saturation changes.
Install KDE Plasma, select the "built-in" color profile, and you're done, no more oversaturated colors. If you want to test how it looks, just use a live boot.