It sounds like your issue might be related to how your Docker networks are configured for DNS and internet access. Try these:

1. Check Network Configuration: Ensure your new networks are correctly configured to allow internet access. Docker networks should be able to route traffic to the internet by default unless specified otherwise.

2. DNS Configuration: Since you're using Pi-hole for DNS, make sure the new networks are properly configured to use Pi-hole as their DNS server.

3. Inspect Network Settings: Compare the settings of old_main with the new networks. Use the following command to inspect the network configuration:

   docker network inspect old_main
   docker network inspect cloudflared
   

   Pay attention to the gateway, subnet, and any custom DNS settings.

4. Check Docker Daemon Configuration: Verify that your daemon.json file is correctly set up to use Pi-hole for DNS. It should look something like this:

   {
     "dns": ["<Pi-hole IP>"]
   }
   

5. Verify Container Configuration: Ensure that your containers are correctly configured to use the new network. This can be specified in your docker-compose files like this:

   version: '3.7'
   services:
     cloudflared:
       image: cloudflare/cloudflared
       networks:
         - cloudflared
   
   networks:
     cloudflared:
       external: true
   

6. Check Firewall Rules: Ensure there are no firewall rules on your host or network equipment that might be blocking traffic from the new networks.

7. Test Connectivity: Run a simple connectivity test from within a container on the new network to check internet access:

   docker run --rm -it --network cloudflared alpine ping -c 4 google.com
   

   If this fails, the issue is likely with network configuration rather than the containers themselves.

8. Docker Network Restart: Sometimes, Docker networks need to be restarted to apply changes correctly. Try removing and recreating the problematic networks:

   docker network rm cloudflared
   docker network create cloudflared
   

If none of the above steps resolve the issue, there might be a deeper configuration problem. At this point, it might be helpful to see the exact configuration of your docker-compose files and the output of the network inspection commands.