OpenWRT + AdGuard Home - OpenWRT itself cannot resolve DNS, clients can

Yes, precisely. There is also a companion AGH setup post, where yaml file is described.

I tested the setup on my router with AGH stopped, there is indeed no fallback for the router to the router's WAN DNS providers. I keep noresolv option 0. Probably to have the fallback, one needs to manually add another forwarding to dnsmasq. Haven't checked.

Overall, why do you want router to go to WAN DNS, not AGH?

Curious, why do you set up this in AGH upstream DNS servers:

Also, the AGH guide suggests to add non-encrypted DNS resolvers (Cloudflare below, or any of your choice) for NTP to AGH upstream DNS servers:

[/pool.ntp.org/]1.1.1.1
[/pool.ntp.org/]1.0.0.1
[/pool.ntp.org/]2606:4700:4700::1111
[/pool.ntp.org/]2606:4700:4700::1001