Melissa and Igalia have been working with AMD and Valve in particular a lot on the AMD color management support, enabling HDR use-cases for Valve with the Steam Deck (OLED), and more. There's also ongoing work within the GNOME camp around VRR, enabling HDR on the desktop, etc.
Err.. no it doesn’t. There are so many bug reports of neither HDR nor VRR working properly with the steam deck. My deck won’t even dock properly with my TV after recent updates.
It’s better than most other linuxes in the sense that it works sometimes I guess.