My pick after searching around is the 8BitDo Ultimate C (link) which is the cheaper version of the ultimate with no dock. So far, it's been working well for me. I just had to restart the Deck the first time after the pairing, since then, it recognize the device all the time.
Stay away from any Xbox Series X/S gamepads. They are cheaply made trash.
I bought the standard version of it for my Deck, expecting it to be somewhat comparable to my Xbox 360 gamepad (which I really like, but which does not have Bluetooth), but nope, it is so much worse...
A friend bought the Elite version, and he also agrees that those gamepads are utter garbage.