Having not played 5e in PnP yet (my group is kinda scattered 😮💨) I have to wonder if Performance is not tied to bardic inspiration or other bardic abilities that used to require performing a song to keep up, much like how casters use Concentration, or if it's simply BG3.
Performance is not an "ability" in DnD I'm pretty sure. It's just something you do with an ability check. You can just go to a bar and play a song or whatever, and roll a performance check. I haven't played Bard in BG3, but I assume what you're talking about is an action you perform in the game that's trying to emulate the feeling of tabletop. I wonder if you can do it around people and make money?
It's a skill, like concentration. It's used like concentration is, with it being checked when you're attacked during a performance for a buff or other bard spell you've cast that requires focus. The game does do this (like, it checks your performance skill when attacked while concentrating on a spell), but instead of actually showing your character playing continuously while having one of these spells cast, you just pick a song to play as a free action to just add flavor totally optionally. Now, in, say, Neverwinter Nights when you are concentrating on a skill, your character will play their instrument until they fail a check or the spell ends completely automatically.
Also: You can make money playing instruments. There is even an achievement to make so much.