hdr works fairly easy now. Not sure about default proton but ge and probably some of the other variants like cachy have it mostly built in. I just use ge-latest for everything via proton plus until a game doesn't work with it before tryig others.

game settings go to launch options and put in:

PROTON_ENABLE_WAYLAND=1 PROTON_ENABLE_HDR=1 %command%

monitor settings make sure hdr is enabled.

I only do dual monitor now but whenever a game can't be on the right screen or does weird sizing shit:

alt+enter/f11 and drag to correct monitor, or

windowed, move to other screen, borderless/fullscreen, or

borderless, taskbar right click and select move then drag to other screen, or

select other monitor from ingame settings

If none of those work it could also be a native linux build which while nice to have tends not to be consistent across games, and forcing proton will redownload as the windows version which I've found will have different screen behaviours compared to native in a lot of games.

Freesync should be in monitor settings if its detected by the system. I've only confirmed it a few times working with ge proton as I don't have many games that both have it and that I remembered to check for it. Usually I do the deck thing even on my desktop and find a config that can hold 90/60/45/30 and set the refresh equal or double manually.