On Mikrotik I have a script that runs every 30sec. If pi-hole not responding, router switches to public cloudflare dns records, otherwise to pi-hole IP.
This setup works like a charm.
P.S. I am using Blocky, but it's almost the same as Pi-Hole.
Don't forget to configure Mikrotik router to act as passthrough DNS server with cache (for performance) and configure DHCP server's DNS to router's IP.