I was having similar problems just the other day. I posted this thread (with no replies) Wireguard in Qubes 4.1
I just changed to HVM and it worked… so thank you! But I also noticed that, unlike OpenVPN, I also need Network Manager enabled in my VPN proxy VM. So both HVM virtualization and Network Manager seem to be necessary to get my AppVM browser to connect via Wireguard through my proxy VM.
OpenVPN seems to work for both PVH and HVM - with or without Network Manager (obviously if I don’t set up my VPN using Network Manager).
So the million dollar question… do you have Network Manager enabled in the VM that is providing the Wireguard network to your browser?