+1 for installing Arch. If you have enough knowledge of Linux to understand what Arch is and why it is, comparatively, a more involved installation. Then you’re probably ready to install it. As was mentioned in another content, long as you know the basics, it’s not as hard as you might think. Also as suggested in another comment installing in a VM or spare hardware is good practice.
As for learning, take the time to understand the commands you’re copy/pasting. Read the man page, see what the flags you’re pasting in to. That might sound daunting at first, and you might not always be able to completely wrap you’re head around it. But you’ll learn more and more over time.
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 has 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 https://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.