

Some things to consider:
Do you have the game-devices-udev package installed? Its udev rules might be needed for some software to detect your controller and its features.
Have you tested for different behavior when connecting your DualShock 4 via Bluetooth vs. USB?
https://github.com/ValveSoftware/Proton/blob/proton_10.0/docs/CONTROLLERS.md
Let’s also remember that average GPU price tripled from 2019 to 2021, and still hasn’t returned, even adjusting for inflation.