mastodon.social is operated by the Mastodon gGmbH, the core body behind the project.

Correct, but there’s nothing special or privileged about it. The others aren’t knock-offs or imitations. They’re all peers.

And? That's the beauty of it, i'm sure there's more to it to your story, but if truly you were banned for something silly, you can join another server (or even create your own!), there's a lot of alternatives.