When I look at my network connection details in Windows 10, if "obtain DNS server address automatically" is selected, the IPv4 DNS server shown is 192.168.1.1 and the IPv6 DNS servers shown are my ISP's. I have them both set manually to Google DNS servers in my router's settings. Shouldn't both the IPv4 and IPv6 servers shown in Windows be the Google servers? Since the router is listed as the IPv4 DNS server, will it use the Google DNS server?
Depends where you set it. There's two places.
1st, under the wan settings you can specify the DNS servers, this sounds like what you have at the moment.
2nd is under the DHCP settings, you can choose to advertise additional DNS servers to the clients.