It can get even more complicated when you have multiple connections on your machine, each with a different DNS server. You'd need to match the DNS server determination algorithm of the operating system to remain consistent, which is one hell of a task.
There's also the fact that there's no DHCP option reserved for DoH/DoT/DNScrypt (yet) which requires some standardisation work.
There's various APIs to read the current DHCP configuration for a network interface so technically it shouldn't be too hard (at least not when it comes to Windows or macOS where there's standard APIs, as opposed to Linux whose modular layout makes finding a standard location for DHCP config difficult).
If you have multiple connections, each of those DNS servers should return the same answers.
If they do not, they should be marked as forwarders for their respective domains. Something like `Add-DnsClientNrptRule -Namespace "domain.com" -NameServers "1.2.3.4"`
The operating system will have this information; an application, like browser, won't.
There's also the fact that there's no DHCP option reserved for DoH/DoT/DNScrypt (yet) which requires some standardisation work.
There's various APIs to read the current DHCP configuration for a network interface so technically it shouldn't be too hard (at least not when it comes to Windows or macOS where there's standard APIs, as opposed to Linux whose modular layout makes finding a standard location for DHCP config difficult).