I have the same issue. Spent collectively about 12 hours trying to troubleshoot it. I've always been able to eventually get a Dualsense controller to work (sometimes using DualsenseX or DS4Windows of course), but Avowed is the one game that beat me.
I finally had to get an 8bitdo controller that just registers as an Xbox controller and that solved the issue.
But yeah, specifically my problem was that all buttons worked fine unless I was in any sort of menu. In the pause menus, LB, RB, B, and X didn't work. The buttons were registered, because if I shook my mouse to switch the UI to PC controls, then pressed RB, it would switch back to Xbox controls, but the button press wouldn't move the menu.
This happened across both Gamepass and Steam versions.
Also, for me it has nothing to do with drift as that Reddit thread seems to suggest. I tried completely disabling the sticks in software and it did not help.