I use a DNS server on my local network, and then I also use Tailscale.
I have my private DNS server configured in tailscale so whether on or off my local network everything uses my DNS server.
This way I don’t have to change any DNS settings no matter where I am and all my domains work properly.
The other advantage is you can configure the reverse proxy of some services to only accept connections originating from your tailscale network to effectively make them only privately accessible or behave differently when accessed from specific devices
Try Matrix bridges or Beeper