Bluesky doesn't have "instances", it has PDSes, Relays, and AppViews. People can run their own PDSes but PDSes are kind of invisible so you won't "see" them. You'll just see the whole Bluesky network as usual.
There are other clients for Bluesky that do the same thing as the bsky.app web app: https://docs.bsky.app/showcase?tags=client