I got here via eth, one thing I miss about eth is what you’re describing. Signing in to a site that knows nothing about me by verifying a signature using my wallet. I feel like bitcoins base layer couldn’t really handle this well simply because of what it is. But maybe nostr or a layer two like lighting? I don’t know enough about lighting to use it directly yet but ideally you’d have control over the keys to your account and the responsibility to store it knowing you have to keep your keys safe or lose access to everything.