Finally, I solved this by moving the steam client version to beta, everything above now just works fine.😊
Is there any advice for tracing problems same like these? I just solved this issue like a headless chicken.
Closing per the last comment.
Nothing extracted yet.
Your system information
Steam client version (build number or date):

Distribution (e.g. Ubuntu): Gentoo
Opted into Steam client beta?: No
Have you checked for system updates?: Yes
Please describe your issue in as much detail as possible:
When I plugged in my controller(ds4/5, pro controller...), whatever native game or steam play game, it only worked for steam overlay and big picture mode, but no gaming.
my ds5 controller configuration and other controllers tried either default or online configurations same like this:

system information, kernel configuration,
udev monitoroutput when ds5 plugging in and out: https://gist.github.com/K1ngst0m/22d3c5c637c629956d691e62ab438e51Steps for reproducing this issue: