@Emil

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

Today:
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.

@Emil

I am using latest version of AppleTv as Homekit Hub and is in TvOs 17.2

Please try this google search:
flic homekit could not complete operation site:www.reddit.com

I am not the only one with the issue

@Emil

I am trying to add an additional Light to the single press action on the flic button in Homekit

So it is in the configuration of the the flic button in Homekit

When trying to add an additional light to flic button in homekit, i get the following message when pressing OK:

“could not complete operation” (In Danish: Kunne ikkefærdiggøre handling)

I can then press Ok on the message, and then cancel to abort the add light

The 4 buttons I have works perfectly, I just cant change their configuration

Have tried to cut power from the flic hub, didn’t help

There are several Reddit posts on the subject as well