So i have a site to site Wireguard VPN between two routers
and I also have a wireless link between the two sites

OSPF cost is set to higher for the wireless link (because the VPN is faster).

But something strange happened the other day. Internet went down at one site. That site lost its (DHCP) IP address. But for some reason, the Wireguard link was still up. It was definitely NOT up, but routeros was allowing me to ping over that interface. The problem was that the site where internet was down was trying to use the remote site as a gateway. It would start sending traffic, and then stop. It kept flapping like that, until I disabled the Wireguard connection. It's absolutely positively NOT possible for the remote site to have a wireguard connection up: internet was down, and I'm not announcing the public IP addresses over OSPF.

Is there anything special about Wireguard and any reason why RouterOS will be establishing a link to a remote site that's NOT the Peer address configured?