I found that the cname record seemed to be the problem. Here someone had the same issue. After changing now to a wildcard A record pointing to the tailscale ip, it all magically works. Thanks for all the answers!

Well the local LLM is definitely a stretch goal of mine hahahah

Thank you for the nod to healthchecks.io, looks great!

This sounds like an elegant solution, will try it out, thanks!

I don't have a problem to always be on the tailnet with my client devices, but it does not work even for this case.

I disabled private dns and it seemed to work yesterday, but today i can not connect to my services again. Any other ideas on how to pin down the issue?

I configured Adguard now as the ipv6 dns server in the fritzbox as well. For now it seems to work, under settings > network & internet > network details for my home network it shows the right dns addresses now. Thanks!

Yes no matter if it works or not, it always returns the tailscale ip I configured with cloudflare, saying it is using 8.8.8.8 as the dns server.

Yes, correct. So far I was able to access the services via : on any device in my tailnet.

Yes, similar to the video guide, I set up a wildcard CNAME record to point to ..net.