I've just deployed a new nostr-login on nostr.band (reload hard please) that has account switching. I've got my real key connected, and also jack in read-only mode. Switching is a couple of clicks. Nostr.band doesn't personalize the experience much, but the concept is working. Switching is log out and in though from app's pov, so it might be heavy depending on the app.
Signing in with extension seems to want to load alby by default and if I close it, it wont pop anything up again
Do you have a screenshot or video of what's happening? There's nothing special about alby there...