OpenVPN isn't necessarily "constant" in that way, it occasionally has to renegotiate as well.
WireGuard does not work the way you imply. It is for all intents and purposes connectionless. There may be a handshake but it's completely transparent. The VPN is always "active" and any packet that tries to use it will handle that negotiation in the background if it hasn't had a recent handshake and so on.
There isn't any sense of it being "disconnected" where traffic would take some other path.