Well, that took the better part of my evening!
So I got an email earlier today from the provider behind my VPS saying they’re gonna stop doing VPS, that I should switch to a KVM, and they left me a coupon for six billing periods (that is, months) of free service for said KMS. Which is nicer than what Centarra did way back then, keeping a hundred euros in service credit for themselves.
And even though I barely have a clue what the difference is between a VPS and a KVM, I did manage to do it with hopefully as few hiccups as I can manage.
Thanks to Dark Kirb for putting my mind at ease, and to Emuz for handling the domain part.