There is an exclamation mark in a red circle, when hovering it says ‘unavailable’ and when clicking, the popup of my question.
I am really stumped by this: I searched for any led01 entry in the whole configuration (all files in the HA configuration directory and subdirectories) and it is nowhere to be found…
I found it. It was being added by MQTT through the HA discovery protocol (it was retained).
I forcefully removed the entry from the MQTT broker and it is gone from HA as well.
It was a miraculous catch (I do not even know how this came to my mind, I think I was looking at the contents of my broker for some other data of an unrelated program and had an epiphany).
My HA setup went over two or three years though major transformations as I was making up my mind on how to deal with the various devices, integrations and my own code (either part of HA or external) - so it must have been a time where light.led01 announced itself via MQTT discovery that it was there.
I am not done yet but I have to balance these changes with the risk of my wife filing for divorce after being stuck in the dark for the umpth time because an exception was not caught somewhere in my code.
Your pointer to the answer is exactly on spot, thanks for following-up.