I meant you should contact the administrator of the other endpoint
OpenVPN has an option to advertise the nameserver. As far as I am aware there isn't such a thing in WG.
DNS doesn't have URL, has IP. And I meant for you to try with nslookup to query some address, e.g openwrt.org with IP of the peer in order to verify if the peer can also serve names,
I don't know how the administrator of your peer has configured it and if the peer is also listening to dns port. But as I explained above it is very easy to test it yourself.
In OpenWrt to do Policy Based Routing you have 3 options:
- mwan3 package
- pbr package
- a set of rules/routes for each internet connection.
PBR is the easiest one.