<hostname>.ts.net should automagically work whenever tailscale is on. You might have to enable something.

If you want more specific, like sub domain names per service, you can set custom DNS records in tailscale to point to a caddy server which routes to the correct port. The caddy server doesn’t have to be the same machine as the service if its on the tailnet.

Getting https involved is a bit more tricky. You don’t need it because its all over wireguard already, but the browser doesn’t know that and will complain. I think official tailscale can distribute ssl certificates across your tailnet but if you’re using headscale you’ll either need to do that manually or buy a domain and have caddy auth for that domain.