I got it working, but I am not sure what actually did it:
I have a setup with AppleTV 4K, Homepod (1 version), Homepod Mini
Ikea Dirigera to control lights and EVE Blinds
All controlled by Homekit
Flic 2 starter kit (hub + 4 buttons)
All has been working great, until I wanted to add a light to one of the buttons, whis failed as described. We have had a couple of power-outs recently
I tried the following yesterday.
Disabled Homepod and Homepod mini so AppleTV 4K became Homekit hub
Waited 5 mins, and checked
Shut down Flic hub for 5 minutes
Turned on flic hub and waited 5 minutes
Still not working
Created a homekit scene in homekit for the desired lights to be activated by single press on flic butten, and was able to apply it.
What actually made it work I do not know, as some of the changes from yesterday may have taken some time to have impact.
I will update if I see the problem again.