Ok, I tried repro'ing again and can on the AppStore version (thx for the steps) but not on the TestFlight version. Since iOS 14 released after the AppStore version, I'd assume that the TestFlight version is using the new detection API while the older AppStore version isn't.
I'm unsure why this functionality is needed in the first place so I'm thinking asking on https://github.com/s-s/dnscloak/issues may be helpful for more visibility.
A reason that stands out to me aside from the ability to have more customizability with dnscrypt-proxy options, DNSCloak is open-source while NextDNS' iOS app isn't. However, NextDNS' "hardened privacy" mode (which only uses servers in jurisdictions with reasonable privacy laws) is an app-only option.