This is because all your traffic is going out the wireguard interface. You have to use a DNS server that can be reached through the tunnel and not local. Otherwise you have a potential DNS leak situation.
You are only going to “leak” dns if you set DNS that is not proton. And im saying “leak”, because from proton perspective, anything that is not their DNS is considered leaking which is not really true. From your perspective, if you are not leaking DNS from your ISP, there is no DNS leak. To test it, go here and scroll down and check the DNS Addresses field. As long as you dont see your ISP`s DNS in that list, you are not leaking and everything is fine.
Just to pick this up again, as I was facing the same issue.
I have several other local services that I have running like Immich and Seafile, does this mean when using the privacy VPN I can no longer have a direct connection locally to these services? Or would it be fine as long as I use a public DNS server that has the same local records?
Also, would there be any way to use some policy routing or something similar to still use my two local AdGuard Home instances as the resolver?
Something to consider. You can set your client(s) to use your AdGuard Home instances for DNS. For public DNS resolution, configure the AdGuard Home instances to forward to Quad9 (or the public DNS of your choice) via DoH. Then for local DNS resolution, you have a few options:
1 - Configure your AdGuard Home to forward local resolution to your UCG. On your UCG, make sure to setup DoH to Quad9 (or whatever you prefer) in case your UCG decides to forward the query to public DNS. Your ISP will see you making an HTTPS connection to the DNS service, but they will not be able to view the details.
2 - Add your local DNS records to the AdGuard instances themselves, and ensure nothing gets forwarded to your UCG.
3 - Point your clients to your UCG for DNS, and configure your UCG to forward to your AdGuard Home instances.
With all options you then, via policy, route your AdGuard instances out the same privacy VPN tunnel for when they forward to public DNS. You could even route them out a different VPN tunnel if you wish to keep them separate from your other traffic.
I believe this might still be considered a DNS leak. But the question is are you okay with the limited leakage? (Do you trust the public DNS provider you’re forwarding to?)