In terms of how LXD gets the external listen IP of a network forward into OVN, the short answer is it doesn’t, at least not anymore.
We used to rely on OVN’s functionality to respond to IP neighbour requests for the network forward’s listen IP on the uplink network. However in OVN 21.06 they broke/removed that functionality if the network forwarder’s listen IP isn’t in the same subnet as the uplink network.
See Can't make OVN network forward working in cluster environment - #40 by tomp
So now you need to ensure that the traffic for the network forward’s listen address is forwarded to the OVN router’s external IP (this can be gathered using lxc network get <ovn network> volatile.network.ipv4.address).
They did add back in an option to re-enable the IP neighbour responders for load balancers using the neighbor_responder option (see https://github.com/ovn-org/ovn/blob/main/ovn-nb.xml#L1895-L1902) but LXD doesn’t use this option at the moment.