You can refer to list of games with HDR support.
As far as HDR in native Linux games, recent changes won't help, but you should be able to get that working with a couple env vars.

This is what I do, I enable HDR on:

• My Monitor's menu (hardware)
• Steam Game Mode
• KDE Plasma monitor config (software)
• Game settings

My monitor isn't OLED, so the difference is barely noticeable to me. Even on my Steam Deck OLED, the difference is not big enough for me. It's nice, but I just can't appreciate it as much as others do. However, I do graphic design so the color management aspect is more valuable to me in a work context, just not so much for games.

If you're using proton, then you're not using the native linux clients you're using the Windows clients.

But, to answer your question, if you want to see if you're using HDR it will depend on the game. For a method that is game agnostic, install mangohud: https://github.com/flightlessmango/MangoHud which will let you see all kinds of information about the game that's running (often used for FPS/temps).

If you'd rather use a GUI instead of editing the config files, you can use goverlay: https://github.com/benjamimgois/goverlay