This answer is completely untested and something I came up with while poking through my phone’s options. But it should work as long as the app in question uses your phone’s DNS settings.

My Samsung phone a private DNS setting. Settings > Connections > More Connection Settings > Private DNS. This doesn’t seem to be bound to a specific connection on my device so I assume this value is used for any. I don’t know if this is available on all modernish android devices or iOS.

One can set up a dns-over-https server such as github.com/m13253/dns-over-https/ and configure it to use a DNS server which is sinkholing those domains. Which it sounds like you already have setup.

You’d have to have that public facing with a reverse proxy and a valid cert so they could reach it while on mobile data, so I don’t know that the juice is worth the squeeze.