The first door is using any axis on the mouse, but it’s easier when you use left-right(horizontal) movement rather than random direction.
The idea is that you’re the one trying to pick lock the door rather than just click and go; The same happens in the storage door lock but since that room has a key the puzzle is easier (the fork one uses a value of 0.52 and the storage with a key uses 2.0 which is way easier to unlock).
If you haven’t tried it before, there’s a bomb in there(storage) so you can pick and avoid the vault puzzle (end the level quickier).