Federation isn’t a proxy. You’re conflating two different things here. If you use a proxy to access a website, you yourself have still accessed that website.

If I access a lemmy community on a remote server, I am not accessing that remote community directly, I am still on my home instance, accessing a local copy. For example, I am still subscribed to boardgames@feddit.de. I could go create a post there. But guess what. Feddit.de doesn’t exist anymore. The only place that post will go is lemmy.zip because feddit.de is not there to federate it out. Is feddit.de suddenly providing me a service? No! It doesn’t exist anymore! I am interacting with lemmy.zips local copy of that community.

It’s exactly the same for a live instance. I am not submitting anything directly to the other instance. Instead I am submitting it to my home server, which is letting the remote server know about it.

You're literally just describing submitting content by proxy. Like, it cannot get any simpler. The only way this would not be submitting content by proxy would be if the home server you were submitting to had no connection to .world whatsoever, and the transfer of content to .world was done without the posting user's knowledge.

That is a simple fact about how federation works. Can you tell me at what point that user has interacted with lemmy.world’s website?

The moment they submitted content to a comm whose instance is Lemmy.world. "It went through their home instance first" is literally arguing that submitting content by proxy excuses one from ToS, which...

Fuck man, really, consult a lawyer. Or articles on Mastodon legal issues for instance hosts.