Glad im not the only one struggling with this. I was able to get nginx to give me the congratulation page via the tailscale ip for the machine but getting that routing to work with my own custom name is giving me a headache. I am probably adding an extra unnecessary layer by trying to use adguard home as a dns rewrite. If you crack it id love to hear how you achieved it.
My theoretical reasoning is. Make adguard be the dns server tell tailscale to use that and then parse all rewrites and dns for the tailscale netwrok through that endpoint (including exit node which is on the same machine).