There is an open standard for logging into websites with other websites' credentials, it is called OpenID and long predates ActivityPub (and is independent of it).
schnurrito
Your specific problem is solved, but just for people reading this thread who may be confused about some concepts:
Your instance of Lemmy or Mastodon, whichever it may be, is just one website that serves as a Reddit or Twitter clone respectively. There isn't a lot of difference between one single instance of Lemmy or Mastodon on the one hand, and Reddit or Twitter on the other. Just like you need to register and log in on Reddit or Twitter if you want to interact there, you need to do the same on any instance of Lemmy or Mastodon you want to interact on.
So what is the concept of federation then? It doesn't mean you can log into one website with the credentials of another website. All that federation means is that the website downloads some of its data (posts, comments, status updates, whatever) from other websites running the same or compatible software, instead of getting all of it from its own users (like Reddit and Twitter do).
In diesem Artikel https://www.heise.de/news/Bargeldlos-Schwarz-Rot-will-elektronische-Bezahloption-zur-Pflicht-machen-10341769.html klingt es so, als wäre es primär eine SPD-Initiative.
You can follow Lemmy communities on Mastodon but that will cause every single comment to appear in your feed, so depending on how much activity they get, they will probably flood your feed. You can post to Lemmy communities from Mastodon by mentioning them, to the best of my knowledge. In either case you can reply to whatever you see on Mastodon and it will appear as a Lemmy comment.
You cannot follow Mastodon accounts on Lemmy.
Kann bestätigen, bin Österreicher und die Existenz des Deutschlandtickets war definitiv ein Faktor dafür, dass ich in den letzten paar Jahren viel durch Deutschland gereist bin und nicht irgendwo anders.