This is true, the collision can be unforgiving at times. It would be theoretically possible to get the character to fit into exact-size gaps in a really quality-of-life way but it would not be easy (I tried... all it did was make all collision glitchy and gross!)
But it's something to aim for, if I ever touch this again.
The jumping issue is actually the same exact issue, because the collision was made specifically to not care which axis is which at all, so solving the first one (by, like, forcing the player to snap to the axis if they're trying to move in that direction and they're "close enough") would also solve the second by the same mechanism (the player would simply snap into the gap in the wall if they're "close enough")