Get MidiView ( free ) from the AppStore. Reboot and use to monitor for any Midi messages (without Logic ) from the device. This can help DeBug and know what Midi message you are trying to map or test (e.g. "Record"). If you do not see the proper MIDI message when you hit Record the issue is not with Logic. ( e.g. Hit play note the MIDI Message, Hit Record Note the Midi Message, they should NOT be the same message.
Lots has been changing with Logic/BigSur and Midi. It sounds like the controls mapping is not correct. Check your controller setting under Logic Pro -> Control Surfaces. I don't know UVI setups but I bet if you explore this area you will find a solution. You may need to delete any old controller settings files and update or us "learn" mode.
CRITICAL: Make sure that you have updated the driver for the UVI or interface ( if used to connect the UVI with 5 pin DIN) . Many older device drivers and MIDI adapters no longer work consistently with Big Sur. Check with each vendor for its OSX support statement re Big Sur and get supported drivers.
Hope this helps