Can someone tell me what I should do?

It doesn't matter when you received the invoice. What counts is what is stated in your contract conditions, e.g. when the next invoice is due.

hase has already told you the solution.

However, I would like to point out that other people besides you also have the right to censor their name - including the support staff at netcup.
Furthermore, I also find it critical to publish the full product ID. It would be nice if you could censor it afterwards.

Quote from MINAMO

which means I am giving the server to a stranger I don't know for free?

Unfortunately yes.