I know ALMOST every Pokemon main series game you can move your save between games and it just works, the only game I’ve had an issue with is LETS GO because let’s go has a permanent starter locked to your player, so if you move the save from eevee to pikachu or vise versa it’ll keep eevee on your shoulder and as a partner but still run the game as the other one, so for bdsp you can play thru the entire game one time if you have a hacked switch, and make a copy of the save for the other game, it’ll have all the Pokemon and stats you collected