After some fiddling around, I managed to solve the problem, and I am posting this for closing this thread properly and helping other people who might experience the same problems.
I do not remember exactly in which order, but after trying a lot of things:
- Disabling Thread in my Google TV Streamer 4K and ultimately power it off
- Power off my Dirigera
- Clear cache, and all data for Google Play Services
- Rebooting Homey
I finally could get Homey on the correct thread network:
From Homey:
And from Android:
I suspect the little key icon and mention “Unavailable” for the Google-B669 thread network is simply because after clearing Google Play Services, Android does not have the credentials for this network anymore.
Now I can add to Homey the whole bunch of new Ikea matter devices I purchased a few days ago and it works really nicely. I still have two threads (Last devices was shared from Dirigera to Homey), as you can see Homey added devices and Dirigera added device are on different thread networks:
Screenshot is from Homey Developer tools, that is really handy for checking more details of your matter devices. For each device, you can View, Ping, Interview or display the thread information:
Above is for one of the Homey added devices, while below is for the Dirigera added devices then shared to Homey:
So it all works as it should now, thanks again to Peter for his help.
Question remain: How to get rid of the unwanted Google-B669 thread to have all devices on Homey thread, but that will be another article, stay tuned 
