The debug log is a troubleshooting tool, and is generated from either the web admin GUI > Tools > generate debug log, or from the Pi terminal with the command pihole -d
With either method, you will be asked if you want to upload your debug log. If you do, select Yes and the log will upload to a server, and you will be give an alphanumeric token. That token allows a handful of people on the Pi-Hole team to access the debug log. The debug log automatically deletes after 48 hours as well.
I’m confused; I thought this [Multiple network clients > Router (acting as the primary DNS server) > Pi-hole (acting as an upstream DNS server)] was the recommended setup. I understand this makes it look like all DNS requests are are coming from the router (because they are). What sort of setting in the router would preclude this behavior?
As explained in the FAQ, some routers don't push the IP of Pi-Hole for DNS, they push their IP. So, the clients send all their DNS requests to the router, and the router sends them all to the Pi-Hole and the requests appear to originate from the router.
Other routers push the DNS of the Pi-Hole to the clients, and then the clients send their DNS requests directly to the Pi-Hole and Pi-Hole sees individual IP's instead of the IP of the router.
I use Apple routers, and they fall into the second category. In my Pi-Holes, I see the individual IP's of the clients, not the IP of the router for the DNS requests to Pi-Hole.
Since your router falls into the first category, you have several options to change the behavior.