That's your handle and it points to the server where your atproto account's data is stored. You can use this same login for other atproto apps and it will all be stored on the server at tngl.sh A username.bsky.social handle just means bsky set up that account and your data lives at the bsky.social PDS. You can migrate to a different PDS and change your handle if you don't trust them. You can host a PDS yourself if you like. I agree it's a little clumsy, but I'm sure friction can be reduced.

The idea is to give users control over their identity, network, and feeds instead of big social platforms like facebook or twitter that choose what content you see and lock you into their closed network.

Oh, that is unfortunate. Bluesky implicitly adds the .bsky.social domain name. Hopefully tangled starts doing the same some day.