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NordVPN is an SSL VPN [OpenVPN], so you can specify DNS settings in the client config [.ovpn]:
Add to the client config → Disconnect VPN → Reconnect
# Set IP to Pi-Hole's DNS server:
dhcp-option DNS 192.168.1.1
# You can also specify your own WAN DNS [OpenDNS]:
dhcp-option DNS 208.67.222.222
dhcp-option DNS 208.67.220.220
# May also be ...
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This is expected behavior. All traffic must go through the VPN for it to be effective, otherwise your local DNS would point the connection towards the internet and not towards your VPN. It is going to be either your Pi DNS server or NordVPN.
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