With a VPN on everything should be going through the the encrypted VPN Tunnel, when the tunnel collapses any thing in transit will be lost does that make sense, Adguard is running your DNS and nothing on the internet works with out DNS. That stated the best order in my opinion is to stop the VPN then Adguard home, but it really does not matter
I use the vpn for everything with very little issues. I only use the NordVPN DNS servers for upstream request. Bootstrap DNS are the next DNS servers if they don’t get a response form the first ones. When you use the Nord DNS it hops IP address about every 10 minutes of so and just have to wait a litter bit to watch stuff.(might have to flush the local machines DNS settings too.)