Something, I just discovered. If I start the service in automate, then, after the error pops up, manually connect the Wireguard VPN, then turn on my wifi to connect to my named wifi network, the Automate service will turn off the Wireguard connection. Then, as long as I don't manually manipulate anything else, if I lose Wifi on that network again, it WILL connect to Wireguard and not throw the error.
I have no clue why this is, but it works. So, basically it looks like for this to work, you need to manually connect to Wireguard the first time, then (assuming you'll have to do this after every reboot) after that it should continue to work.