After some extensive googling around I managed to install the ISRG Root X1 certificate (as described here), and the Let’s encrypt test site says everything is ok and valid.
That didn’t help F-Droid in any way though. It still threw either ‘no mirrors available’ or the aforementioned certificate error (depending on the switch for old/new XML format in Settings).
@ throwaway69, you advice worked well! F-droid classic really fixed the issue. Thanks!
P.S. The store is still nearly empty, very few apps are available. Not sure if there’s anything I can do with it.