A global login wouldn't break a defedaration, it would simply spit out some error such as "Your credentials are invalid, your home instance is not federated with this instance."
I got into a link posted somewhere in a post that took me to wikipedia's mastodon but I'm registered on mastodon.world. And this has not been a single instance, happened plenty of times with other lemmy instances.
Jfc, what did you do? Take shelter?