Using a PSK alone doesn't make WireGuard quantum-safe. The security of the key exchange mechanism in WireGuard, which relies on the Diffie-Hellman protocol, is still vulnerable to quantum attacks.
If an attacker were to obtain the PSK and use a quantum computer to break the Diffie-Hellman key exchange, they would be able to decrypt the VPN traffic.
This is currently the thought-process and main reason behind why PQWG (Post Quantum Wireguard) are actively being researched [1].
> Using a PSK alone doesn't make WireGuard quantum-safe.
Not sure what you're trying to say here. If you share the PSK out-of-band, securely, then wireguard is quantum resistant (I wouldn't say quantum-safe, because I'm not that optimistic).
> If an attacker were to obtain the PSK
Indeed if the attacker obtains the PSK then obviously the PSK isn't going to help you.
Please be careful in your quoting. The page you linked says "post-quantum resistance", not "post-quantum security" (which would be a much stronger claim).
If an attacker were to obtain the PSK and use a quantum computer to break the Diffie-Hellman key exchange, they would be able to decrypt the VPN traffic.
This is currently the thought-process and main reason behind why PQWG (Post Quantum Wireguard) are actively being researched [1].
[1] https://ieeexplore.ieee.org/document/9519445/