An update on this. My new mouse's wireless Dongle is treated as a gamepad by Steam and preventing my actual controller from functioning. Unplugging this allows controllers to work just fine in Proton-ran games. This still shouldn't be the case since in every other context the controller works just fine, but this seems to be a more specific issue.
proton 9.0-4x1 2025-03
OS: OpenSUSE Leap 15.6
Kernel version: 6.4.0-150600.23.38-default
Tested with Proton 9.0-4 and 8.0-5 in a handful of different games that run through Proton for compatibility.
Very recently any game ran using Proton no longer recognizes my gamepad inputs (8BitDo Pro2).
The controller tests fine through the OS, works fine in Big Picture Mode, in the in-game steam overlay, and with any other game ran natively.
Changing the input method of the controller does not make a difference (Wired, Bluetooth, Xinput, or DirectInput modes).
Using steam input to translate the input does not make a difference.
Non-gamepad input sources work perfectly fine.