It doesn't depend on fediverse software.

Whatever is the fediverse software, your credential will only work on your instance, your fediverse home server.

More exactly, your credentials are stored in the database of a server. If you have created an account on lemmy.world, you can't login on lemmy.zip (another server), nor mastodon.social (another server...), nor peertube.org, loops.xyz...

Because they are different server, they don't share the same database, they have their own database. Your credentials are only on lemmy.world, so other servers don't know who you are.

However, there are several technical solutions, that allow cross-platform login. They are not easy to set up :

LADP

We could create a LADP, that's a huge database with users credentials. For example, yunohost. When you install several apps with yunohost, you don't have to create another account for each installed apps because those apps share the same database where your credentials are stored.

OAuth

There is another method : OAuth. I guess it talks with severs but i can't explain how it works. Piefed use it for login with already existing account elsewhere as mastodon (?). We could log in to piefed with a mastodon account, or google.