Wireguard will keep contacting the remote server. You'd have to delete the wg0 interface or delete the default route for packets to go out via ens0. Wireguard only has "connection" in a sense that it caches some runtime information about the peer's endpoint, but endpoint configuration is static.

I guess, too much magic automation on top of this is not the best thing for opsec, including having some daemon that can disable your wireguard interface or reconfigure the network if it doesn't like something. You want your network configuration to be static and predictable, regardless of some temporary failures. Basic wireguard kernel primitives will give you that.