Andi has a point, but the lever you press in is pretty frail. Still, his pic is very useful here.
Seeing your vid, I reckon many of us may have been barking up the wrong tree. It seems it may be nothing to do with the locking mount mechanism whatsoever. You key appears to unlock that perfectly. Whether anything is then happening when you pull the LH unlock lever isn't clear though - this pulls the lock bar to the left (the vertical bar with 2 small mounting screws in Andi's pic, shown as parts on a earlier vid). You should be able to check this visually, with a light/mirror if necessary. You see, when you forced the unit into the mount, something had to give to allow the release mechanism to permit it's two lock tongues to rise en-block. No point in me second guessing what might have happened until we know whether the lock bar is moving correctly. You may even be able to move it manually, from the rear.
If the lock bar is pulling back correctly then my suspicion is that the release lever, which lifts the two locking tongues that you can see in Andi's pic above (just above the words BMW Motorrad) must have somehow broken internally within the sealed plastic structure. These 2 tongues cannot lift the block unless the unlock bar has moved left, sliding in those 2 slots.
Anyway, please report back about the lock bar situation first. Please make sure we now define clearly between the locking mount mechanism & the SatNav release
Good luck.