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.

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?