The error doesn't pop up just because you have a VPN connected. It pops up when it can't actually communicate with the car. All it's doing is adding some extra text to the error message if a VPN is connected.
Wireless Android Auto communicates to your car using Wi-Fi Direct. Something is preventing your phone from communicating with the car. Sometimes it's an improperly configured VPN.
Does your Wireguard route all traffic through the tunnel, or only traffic for particular IPs? If it works fine when your VPN is off, that means it's an issue with your VPN configuration. The Android TV version of Wireguard lets you select just specific apps to route over the VPN - does the Android phone version support that?
For what it's worth, I use Tailscale and haven't seen this error.
