I second 8bitdo. I have the ultimate bluetooth model and I love it. That one can switch between bluetooth and 2.4ghz. Unsure how multiple controllers using the dongles would work though.

I've been using the 8bitdo ultimate but I've had a few issues with it over time. For starters the rb button sticks, which I've been able to work around using the back paddles, but it's still not ideal. Recently though I've had a few games misinterpret the buttons, playing through animal well the a and b buttons performed the same action so I had to get my old 360 wired controller out to play through it. Looking in the software (only available on phone and windows, no Linux support as far as I'm aware) showed no mismatch of setup or anything so no idea what's happening there. Playing death stranding recently also had issues, it was as if it was trying to switch inputs from the controller to m+kb constantly.

I have 4 of the 8bitdo controllers (various Bluetooth models) and games have varying levels of support for them. Sometimes all the controllers show up as 1st player, but mostly steam handles it fine. I've also use Microsoft branded controllers in the past with 0 issues, but then you're locked into to that as mixing those with playstation or 3rd party ones can lead to the same player mapping weirdness. Also, the Xbox variety needs a 2.4Ghz dongle to work with the deck, but I've found this to be superior to Bluetooth in crowded environments.

Official Xbox series controllers are relatively cheap for their quality (~40 dollars on sale) and there is an official Xbox dongle that allows for the connection of I think up to 8 controllers with a pairing button. I have not tested this configuration extensively but I think the dongle handles a lot of the logic so it should work better with worse drivers. Also when setting up everything one must just press the pairing button on the dongle and on each controller to get everything setup.

I have a gulikit king kong pro 2 (I think I got the name right). Been using it about a year now, works good on linux (Nobara). Has various modes for different consoles and phones and hall effect sensor sticks (which wont have stick drift) which was the motivation for trying it, along with the lower price compared to the official Xbox controller. Came with a nice hard case and rechargeable lithium too.

Been pleasantly surprised so far.

I have been using ps3 controllers on Linux for a couple of years now. They are dead cheap used but you might need to replace the batteries if you need to use them wirelessly. The drivers were included in popos, so plug and play basically. Just get a compatible bluetooth USB dongle, or maybe the deck already has Bluetooth? The original ps3 controllers are very sturdy and work reliably. I would still be using my old ps2 controllers, which are basically the same, but the usb adapters seem to brake way to often and wireless play is rather convenient.

If your top priority is connection stability (and latency is right behind that), consider going wired with a USB extender and a big USB splitter at the couch-end. You'll save a bundle and the connections won't ever drop