Not GP. My guess is that they’re self hosting this at home (not on a server that’s on the internet), and Tailscale easily and securely allows them to access this when they’re elsewhere.
Even if you are self hosting in the cloud or on a rented box, Tailscale is still really nice from a security perspective. No need to expose anything to the internet, and you can easily mix and match remotely hosted and home servers since they all are on the same Tailnet.
I host at home and can access the things at home just fine by having the server as DMZ in the router, or whatever it is called these days. This doesn't really answer what Tailscale does more than port forwarding. If it punches NAT, that sounds like it actually makes you rely on a third party to host your STUN, i.e. you're not self hosting the Tailscale server?
Yes, it does NAT traversal. If you don’t trust Tailscale servers, you can host the open source equivalent, Headscale (headscale.net) and use the open source Tailscale clients.