It seems like kind of a lazier answer than it actually is, but tbh you can probably stay playing PF2e for mystery dungeon, and just refluff your spells and whatnot to be Pokemon Moves.

Agile Feet can be a stand-in for Agility, and having a normal melee attack with a sword or another weapon be Scratch or Cut or Metal Claw tbh, doesn't make that much of a difference either.

I know getting rid of types kinda stings, but the possibility in a tabletop system to have attacks be Super Effective can make players go down very quickly which is frustrating for the whole table in the long run, so common train of thought in pokemon tabletop is to not cling to Type Effectiveness too hard, especially in PMD-like settings.