Shimano Deore hydraulic brake problem
The part that popped out is one of the pistons.
There should always be a bleed block in place between the pistons when bleeding the brake. Immobilizing them this way is what prevents overfill and also prevents the pistons from popping out if you go to squeeze the lever as part of part of the bleed procedure, both of which happened here.
Excessively narrow pad gap is the main symptom of overfill.
Bleed them again with the block in place and everything should be good.
The piston that came out probably went back in clean and lubricated, while the other one remained however it was. That kind of thing can cause uneven pad wear and adjustment weirdness, as one piston moves more readily than the other. You could try addressing it by intentionally overextending each piston in turn and then cleaning them with a cotton swab and alcohol. Removing them all the way isn't necessary.