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

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 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!

Yes, correct. So far I was able to access the services via <tailscale ip of the host>:<port> on any device in my tailnet.