I mean by this, is there any website that with one sign up would allow you to have a matrix account, lemmy account, mastodon account, etc. If it couldn’t be done with just one url it could be made a thing where it would be service.website.tld (so an example would be lemmy.myreallycool.website). Is there anything that already exists like this? I think it would be really cool to just have one home server for everything that you need, and to also have the same identity on all platforms. Another actual practical application of this I can think of is if you want to message someone you know from lemmy but on matrix you could just change the domain (ex: @username@lemmy.myreallycool.website to @username@matrix.myreallycool.website) or something like that. I know that one of the big appeals of the fediverse is that the accounts are interoperable but I still end up using a different account for my mastodon and lemmy accounts for example. I’m genuinely interested in something like this as I think this would be a really cool idea.
I think a true unification defeats the purpose of federation. That said, I have been using Lemmy Handshake to sync my subscriptions between accounts. I generally use one account to login, but sometimes an instance has technical issues or content seems to be missing so I like having a backup option in a pinch.