Do you have Steam or ds4drv running in the background?
If so, make sure neither are running, then try again.
I really don’t know then, you can try this which I’ve found to sometimes fix dualshock controller shenanigans:
ds4drv --hidraw
You could also try leaving ds4drv running and seeing if that makes a difference.
I haven’t been, I’ve just found that running and exiting ds4drv happens to sometimes fix controller issues.
I’m not really sure what else there is to try, does the controller have any different behaviour between wired and bluetooth mode?
Edit: Also, do L2/R2 move the target around in addition to the function they’re supposed to do? You might need to swap the action of L1/L2 in the game settings to test that.