I do not follow.

You will never own the DNS resolve path. You will need to trust anyone. The internet is based on 12 root DNS servers, hosted very secure anywhere by IBM. And because this is not enough to handle every request the DNS has a hierarchical cascading.
Simplified: Root DNS servers - Regularity DNS services - ISP DNS Server - Local DNS Server - Client.
And no matter what you will only have access to secure your local server. This could be a bind, a DNSMasq, a full blown Windows AD or a AdGuard Home -> But in every case, if the local server does not know the Hostname and the FQDN is not local, the DNS should ask the next one (Forward DNS Server) and cache the result for the next request.

Open source here means 'you can download it, install it and use it'. No payment at all.
You should not Internet access to DNS Servers of your DNS server, because they are outside.
Even with Tor DNS, the request will at some point be resolved by an outside server. And this is good. How should every server in the wold hold every domain-ip mapping?

That is not the point.
The point is that you can use 'AdGuard Home' for free in your home network. And if you are willing to participate the development, you know they will use it also in their paid services. Open, transparent, fair.
As you want to use it for free, you are not allowed to use their provided DNS servers. So it should not be your problem if you can trust them or not. Your part is to download, audit the source, compile and use.

It is the same as using ipset or geoip from your first post.