Thank you for clarifying(and sorry for the late answer).

For you (and anyone interested) I will answer the questions you asked.

Are you going to close upon any legal threat, or only upon a certain degree or size of threat?

If the legal threat is real(they have a real chance to win in a court) and there is nothing I could do(come to an agreement, move the hosting to another server etc), then I would close the server.

From the US only, or from any country?

Server is hosted in Germany

Will you close instantly, or will you guarantee a Minimum Survivability Timeframe for eg.: helping users to migrate away, like Mastodon’s covenant does?

As long as there aren't fines for keeping the website up or I get arrested, I would give a notice, so users can move to another server.