No, ActivityPub doesn't share your login credentials with other websites, nor is it a single-sign-in service.
It's a content sharing protocol that lets websites syndicate content. AP will let you see content from PeerTube channels on blahja zone, as if it were originally posted there, if BZ is currently sharing content with the PeerTube site you're interested in.
AP is why you can see content from lemmy.world on BZ. It's why I can reply to you from lemmy.ca. But it won't let you sign in to a PeerTube website, or even other Lemmy-bases websites, any more than it will let you sign in to Facebook.