I am just curious if you enter a ultra wormhole and it is one with that has a legendary Pokémon and you didn’t have enough ultra balls but you never initiated the battle does it count as me needing to go beat the elite four again?... because I may or may not have done that...
No, you do not need to re-challenge the E4 in order for wormhole legendaries to respawn. As long as you don’t catch the legendary, your chances of finding it is the same no matter how many times you encounter it.