The "just works" Steam Controller(s)

Hope you don't mind me asking here. I just don't want to wander into some place where they threat you primarily as some gamer - without much knowledge about Linux - which I basically started using at 9yrs and have been developer, sysadmin, netadmin etc for the government.

So, I'm not a gamer. My workstation (mainly server) can take anything. When I saw GTA5 at a friend's house I just bought a PS3 at closest store, because, well, looked awesome, and well they had that package with FIFA too so, great. Those 2 games (and some CS back in the days then being LAN party main responsible, had to play some).

Now, I like running benchmarks, and it has been funny to see both Vulkan vs DirectX12 (say Shadow of The Tomb Raider) and purely DirectX games like GTA5 and FIFA 21 (no PS3 version) outperform the latest Insider Build of Windows 10, using Steam Proton on Linux. So one day, just to try, I connected my PS3 controller to it, and voila when pressing the PS button, Big Screen just popped up and could use exactly the same buttons as I used back then. However the (genuine) PS3 controller needs a cable, or hacky Windows-only (as far as I've seen and even that a hassle) and main code needed is archived on GitHub etc. So no thanks.

Basically looking for genuine, good, recognized controllers that aren't obsolete for Steam anytime soon (the Steam Controller seems to be... no more), and just works with a genuine dongle that can drive 2 controllers at least. Preferably RF and no Bluetooth(?). Don't really want Bluetooth, but well, you tell me. My workstation has no Bluetooth (10 Gig Eth is my way). All my RF stuff works great. I don't need explanations here for hacky solutions to some project that suddenly is inactive and e.g. doesn't work on never kernels, because my GF is gonna use it and simply want to press a button, and I want to make it as easy as her Switch...

And yes I've Googled and no article or reddit post really mention properly other than "this works, that works if extra dongle..." and so on. Some even have the headline "Best Linux controllers 2021" with zero specs or info about actual Linux support (e.g. official or not?).

I really like the PS3 controller. I must say. Only used that, PS1 and well Nintendo 1 :D but briefly an Xbox 360. Got used to it for a couple of FIFA matches. But really, anything, if == 'exists', very much appreciated

Requirements:

1. Genuine (branded) good controllers (PS or XBox I guess)
2. Have an official dongle that the Linux kernel just recognizes and doesn't need 1 dongle per controller. If Steam is the only software actually having it all implemented doesn't matter, as long as it works on Proton Games like GTA5 and FIFA just like my PS3 one with cable
3. The controllers just find this dongle and pair, as said preferably over RF (isn't that what consoles use?) so no mess with Bluetooth stack
4. Range at least 4 meters (no obstacles)

Now would be great with something that just paired with my Logitech Unifying mouse dongle, if any good stuff there. But range for that seems bad.

Thanks a bunch!

And of course if there is a good alternative here, it'll work on basically anything, so. Win-win.