The mode button on the motion controller will beep signaling it’s being pushed but nothing actually happens

Same problem Im having, did you find a solution?

I’m also having this issue.

I will take a stab at it... this seemed to fix other "weird" issues in other posts.
Try this.. Turn on MC, Goggles 2 and the Avata, go into the Googles 2 menu (Settings > About > Reset All) and reset all settings. Re-bind the MC and Avata if neccessary.

If that does not work try reflashing the Firmware on the motion controller using the DJI Assiatnt 2 (Consumer Drone Series) application.   I have never done this but this is what I would try.

If that does not work, contact DJI Support / Put in a case.
Since the MC is not covered by Care Refresh, you will more than likely need to send the entire thing back to them for a repair/swap. (just guessing)

I have same issue