The controller thing is definitely a PSO2 thing and I’ve experienced it.
Basically, PSO2 only responds to the first controller you plug in or activate wirelessly from the moment you sign into Windows.
If you disconnect your controller for any reason or your wireless controller disconnects itself for inactivity, PSO2 will no longer work with any controllers you plug in or activate for the current Windows 10 signed on session.
Signing out of Windows 10 and logging back in or simply rebooting your computer will allow PSO2 to use the controller again.
This happens to me, exactly how I described, 100% of the time.
Just as the OP stated above, every other game or application that uses the controller is fine with it, whether you disconnect and reconnect it or not. Even in the middle of a gaming session.
If I accidentally disconnect my controller playing PSO2 on Windows 10, gotta relog onto Windows. Haha.