but if an agent automatically accepts an EULA for you, is it binding?

It would have to be. And it's not new in the law at all. The principal-agent problem was one of the main enablers of the golden age of piracy. But that doesn't mean it isnt a solved problem now (in the law and practically)

> principal-agent problem

Here the agent is not a person. It's unclear this principle holds legally

This is a binding from service perspective. The agent use case is being highlighted in this example, however in practice the server does not knows what/who the client is. In fact with API's (user not present in loop) just notifying is good enough based on what I have been told by company legal teams in the past.

Ideally the agent is supposed to be responsible to surface its own TOS and the downstream TOS to the user. In other words most likely the agent is on the hook if this goes to court

This has never been tried in court, though, at best it probably just protects mojang from liability for banning your server from the IP address entry box (that's a real thing they do) if you don't obey