Own a Microsoft Xbox Series S controller with v2 Microsoft Wireless Adapter. Even after the August update, the game still does not see my analog triggers. The default configuration is absolutely terrible. R3 is pause, RB/LB do nothing, Y brings up notes... its just all messed up. Is there anything special I need to do to get it PS2 level controls without downloading a fix for this?

Update: I found 2 fixes so far.

Fix #1 (Easiest)

I plugged the Xbox Series S controller in with USB. Worked 100% after that. However, I am wired.

Fix #2 (Costs $)

I bought an 8BidDo Wireless Adapter (Red). Sync'd up my PS4 controller to it. Set it to Direct Input mode, configured my controls, and everything was working after that.

Bit of a late reply, but I have the exact same problem. Xbox Series controller connected via Microsoft Wireless Adapter. The game will NOT recognize any analog trigger input, no matter what.

I also have a non-GoG version of SH2 and SH3 installed and those games have the exact same problem.

Download and run XInput Plus.
Set Target Program to sh3.exe.
Go to the DirectInput tab and check Enable DirectInput Output.
Assign Right Stick to Z Axis/Z Rot.
Assign LT/RT to Button11/12.
Assign DPAD to Button 13-16.
Click Apply and a DLL file will be added to the game directory.

should fix the issue from pcgamewiki