I am also experiencing DNS issues using a Wireguard client file on my GL-MT1300 using an upgraded beta version of the firmware openwrt-mt1300-4.1.0-1107-1667792228.bin. I also experienced the problem on older versions of the firmware.
The router seems to use DNS servers from my VPS, which is in this case from the network Vultr, instead of the DNS servers specified by the Wireguard server. When I connect directly to the Wireguard server from my laptop, instead of connecting to the Wireguard server at the router level, the correct DNS servers are used.
To setup the Wireguard server I have used GitHub - trailofbits/algo: Set up a personal VPN in the cloud to create a Wireguard server on the cloud network Vultr. Looking at how that script generally sets up DNS at algo/config.cfg at master · trailofbits/algo · GitHub, it defaults to Cloudflare along with dns adblocking.
I am testing DNS using DNS leak test. Free check. I have no idea which steps to try and copy here to resolve the issue.