Pi-hole connected to the internet, but using manually setting the DNS on the router to the Pi-hole results in a "Bad Config" Error on Browser

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Having AdGuard as your second DNS allows traffic to bypass Pi-Hole and is not recoimended.

Why should Pi-hole be my only DNS server?

Reduced Ad Blocking Capability The main reason you should Pi-hole as your only DNS server is that you will see increased performance in the blocking of ads. If you have two DNS servers (Pi-hole and something else), your network clients may not always query Pi-hole for name resolution. If a query happens to be answered from a non-Pi-hole DNS server, your block lists will not apply (since that DNS server doesn't know about them). All Queries Need To Go Through Pi-hole First Since other DNS se…

You may find success using the Pi-Hole as DHCP server.

How do I use Pi-hole's built in DHCP server (and why would I want to)?

Using Your Existing Router For Network-wide Ad Blocking You might not need to use Pi-hole's DHCP server: In many home environments, your router also functions as your DHCP server. In this case, you can often set Pi-hole to be the DNS server for your network clients in the router's DHCP (or LAN) settings page, which allows all of your network clients to block ads simply by connecting to the network. Setting it up this way is also what makes Pi-hole very powerful for network-wide ad blocking. …