Pi-Hole cannot resolve any request

This is not the way it works. The primary isn't strictly a primary, and the secondary isn't strictly a secondary. Given multiple DNS options, clients will use any of them.

This seems odd. The internet connection for the Pi should be independent of the DNS server in use. For example, on the Pi if you ping -c5 8.8.8.8 , no DNS resolution is required and the ping should go directly to the IP. It is only when you ping -c5 dns.google that the DNS resolver gets involved to provide the IP 8.8.8.8.

You will need to do some more work with your router to get the Pi back online.

Edit - one more thought. What is the nameserver in use by the Pi:

cat /etc/resolv.conf