I tried this on Ubuntu 22.04.2 with a wired Xbox 360 controller and the latest Steam beta client and wasn't able to reproduce the issue. Are you using the stock xpad driver that comes with Ubuntu?
I use the default xpad driver that come with Ubuntu 22.04.6 LST: 5.15.0-67 kernel from official ubuntu.
I think it's OS/driver issue. My steam controller also doesn't work after suspend and resume unless physically reconnected or reboot. Arch 6.3.4-zen1 kernel
Nothing extracted yet.
Your system information
Please describe your issue in as much detail as possible:
Gamepad usb/wire plugged not recognized after suspend and resume the system. You need to reconnect physically for Steam see it. This not happen with old version of the client.
I use a X360 Gamepad wired official.
Steps for reproducing this issue: