I’ve spotted that on Friendica, another instance recognizes somehow that you’re a Friendica user from somewhere, and kind of logs you in as a remote user, if I remember things correctly.

Wondering if there’s any standard or protocol or approach either being discussed or already adopted, for such kind of logins in background as a remote user?

IMO this is how Fediverse and decentralized social networks in general should work. Otherwise we end up constantly logging in on multiple instances. It’s a pretty common thing when someone posts a link to a profile or a post on another instance, and even mobile clients such as Tusky sometimes open those links in browser. Who have tried Mastodon remote following or voting, knows it’s a pain.