I’m happy to be able to answer my own question, since it turned out a repair wasn’t necessary :o)
I found some suggestions elsewhere which made me:
a) tap “forget this device” for the bluetooth pairing for the pencil
b) reboot the iPad (possibly not necessary).
c) insert the pencil’s connector in the iPad to be happily surprised to be asked if I wanted to pair the pencil.
d) I did, and now it’s working fine again.
So, try re-pairing with or with out a re-boot if you experience something like what's described in my question.