The answer is a bit complicated. Linux has a long history with HDR where you would need exact software and hardware, or else no HDR... Just know that it will get easier because the ball has already started to roll in the correct direction.
But the shortest way I can say it now,
If you use Valve's game mode, (which is possible to get either using steamos, bazzite, chimera OS, nobara, or you can manually set it up. You should be able to get it to work. This should work for windows games that support HDR. AFAIK there are no Linux games yet supporting HDR. It should be possible to get videos playing with HDR also, but that would be an exercise for the reader, or wait until people make it easier.
Please correct me if I am wrong, but I currently believe the newest version, of KDE and Gnome are now HDR ready. If I am wrong you might just need the newest beta which will become stable Q2 this year.
Playing videos, I believe the newest version of MPV just got HDR support. With more apps incoming.
Anything that let's a gamepad or a remote browse your videos? AFAIK not yet, but be patient, as this is all new
Yes, my wife used to work in the ER, she still tells the same stories over and over again 15 years later, because the memories of the horrible shit she saw doesn't go away