Gaming

Portables are the best for this, imo. Steam Deck or a used 3DS are my choices. The latter is easy to mod and play all sorts of games including the gigantic DS/3DS library.

I find both systems clutch for the suspend function. Lets you pick right back up where you were. I will say the 3ds is much better at this with clamshell design that suspends on closing the lid and it's battery life in suspend is fantastic!

I also find stress relief games. Mindless 3rd person action games for me. Mad Max was great because I could drive around picking fights or crashing stuff. The Batman Arkham games and the Shadow of Mordor games are other great examples for me. I have not found any relaxing "cozy" games that work for me. Nothing has really grabbed my attention enough to stick with.

game without [being exhausted of the] screen

There is your answer: if screens exhaust you, do something without screens.

Games are supposed to give you a good time, reinvigorate you, and prepare for your "real life". If you're sick of screens, then pick up pottery, or squash, or hiking, or skydiving, or cooking, or... thousands of activities out there to have a good time without a screen.

having a huge backlog

That's work. Just don't. Do stuff that makes you feel better, not just tick a box in a backlog so you feel slightly less bad.

That's the neat part: I don't. I've played so many games I see most of them as minor changes from games I've played before. Most of them do not do anything interesting for me to invest my time in an experience I've already basically had. Very few games manage to feel different.

But if you are exhausted at the screen, touch grass. Playing video games may not be the vacation you think it is, you may need to go outside and spend more time doing things that are different from what you do most of the day: eg your work, your sleep and your main hobby. Go pick up hiking. If you find hiking boring, get a RC trail car and do rc hiking. If you really need that brainrot current popular fps vibes: go do hiking with toy guns: airsoft/paintball

I know this is not for everyone, but may I suggest you to try Hoyoverse games?

Since they are designed to be played both on desktop and mobile, the game play session can be short but still meaningful.

At least this is what I do. I still play other indie games but Hoyoverse really made be forget the need to buy "AAA" games that are designed to waste players' time.

Well, I don't have a desk job and I'm on console. So while I can sympathize, I'm not really able to offer advice.

I work full time at a computer. I have two jobs, so I put in 68 hours a week (second is 28 hours a week, no overlap).

I have no issues with eye fatigue best I can tell, that or I've just gotten so used to it. I will note I do have the blue light filter on my glasses lenses my optician recommended.

i can't play anything that requires more than 0 minutes of my time in a session because i have extreme levels of adult ADHD or something

I play pretty much exclusively on handheld these day. The last thing I want to do after a long day working, is to sit at my desk some more.

I have a Switch and a Steamdeck, both are fantastic for different purposes, and both let me game while relaxing on the sofa or anywhere else.

I usually bring one of then when I travel for work as well, great for killing time in airports or while flying. I'd highly recommend the Steamdeck for your situation - it's definitely worth it.