At least that points you to the problem: firewall somewhere.
Try a different port with your netcat test, perhaps? 51820 is the well-known WG port. Can't imagine they'd intentionally block it, but you never know.
Maybe Hetzner support can offer more guidance? Again, I'm not sure what or how they do network traffic before it gets to the VM. On all of mine, it's just a raw gateway and up to me to handle all port blocking.
If you figure that part out and are still stuck on the WG part, just shoot me a reply.