So I searched a lot, and troubleshooted a lot, and followed many guides. I got Tailscale (as an Exit Node) and Pi-Hole running on Ubuntu in my Oracle Cloud.
At home I have the same thing running (Pi-Hole and TS) and whenever I connect to my home's Exit Node, DNS queries go through Pi-Hole. I am unable to do the same on Oracle Cloud.
I can use the instance's public IP and manually set that as the DNS on devices and that works, but I don't want that type of functionality. I played around with setting the Tailscale IP of the OCI as a custom DNS server in the TS Admin Console, and enabled to override... this does DNS resolving for every device on the tailnet, something I also want to avoid. Splitting also doesn't work.
I'm just trying to create an Exit Node backup with Pi-Hole working. Any advice?