From one of your devices can you check what DNS server they are using? It sounds like the router is setting itself as the DNS server. This would mean all your devices would list your router’s IP address and the DNS server. This is a different setting than the DNS server that your router is using.
If that’s the case you tell your router to tell your devices to set the DNS server to the IP address of your AdGuard Home device. Alternatively, you can manually set the DNS server on your devices.