Will I still need to consider multicast DNS if my DNS server is on-prem (Pi-Hole + Unbound)

Multicast DNS is separate from DNS, so even if you have Pi-Hole, you'd still have devices using mDNS. It's possible to route mDNS across separate IP networks seeing as how there's mDNS relays across VLANs which would suggest Wireguard could support Multicast. Other things use Broadcast (e.g. WoL) which is a bit more challenging to forward across IP networks.

I'm not familiar with GRE so I couldn't comment on whether it's possible or not. I guess it all depends on how confident you are with your networking skills. If you get it working, you should definitely document it and share with others.

I didn't quite do what you did, but I ran HA in a Kubernetes cluster which was logically a separate IP network. I had to setup the container with multiple network interfaces and specially craft the route table to forward broadcasts + multicast traffic to the correct network.