This looks like a Wireguard issue, rather than a Pi-hole one.
You should probably consider to also consult forums specialising in Wireguard.
That said, from what I glance from your config, you did not configure Wireguard with any rules at all that would route traffic from the Wireguard network to an interface with the required connectivity to reach 192.168.13.47, as you are missing any PostUp/PostDown rules, making this look similar to Wireguard VPN not working between Android and PiHole - #6 by Bucking_Horn.
This does note seem to be the case, as you are not using your Pi-hole's wireguard's IP.
If your machine running Pi-hole would have a wireguard interface itself, you should substitute DNS = 192.168.13.47 with that wireguard interface's IP.