How does pve-zsync work under the hood?
Does it rely on SSH?
If so, how does the source authenticate with the dest?
Does it use a private key and where it this key stored?
Yes, it uses SSH under the hood - you can read the source code under [1] if you want to learn more about how pve-zsync works.
The SSH key is simply the default SSH key for root /root/.ssh/id_rsa