If your router allows it you can set your gateway IP from the router (i.e. 192.168.1.1) as the second DNS address in the DHCP settings. So your routers DNS settings would then act as fail over in case your pi-hole is down. That’s at least how I have done it on my ISP router.
Nice, did the same for some services I run at home. Now in the process of migrating my stuff on my vps from docker compose to quadlets. It’s a bit more involved but worth the QoL stuff quadlets bring with them, like automatic updates and systemd integration. I’m curious, which is your Linux distro of choice to run your podman quadlets on?