I’ve never used network manager on a server and don’t understand your routing configuration, im assuming you have wg0 configured to have a default route (ip route list).

You should be able to connect a docker network to the vpn by using a macvlan insted of a bridge type network and set the parent interface of it to the wg0 interface.

docker network create -d macvlan \ --subnet=<internal vpn network>/24 \ --gateway=<gateway ip> \ -o parent=wg0 vpn-net

modified from the docker documentation

Make sure the allowed ips in the wireguard configs are set correctly.

You can also do ipv6 like this, see the end of the linked documentation page.