The OS ought to let you deny internet access to an app entirely, but DNS-based adblocking might solve your problem: https://mullvad.net/en/help/dns-over-https-and-dns-over-tls

Then don’t use an ad supported app? I have one as supported app on my phone - Overcast. The developer created their own ad platform and serves topic based ads based on the podcast you are listening to right now. Ironically enough I started to pay for a subscription even though it didn’t give me any real benefit just to support him until he started having ads.

I’ve found a lot of useful podcasts from the ads.

I’m gonna be That Guy for a minute: if you enjoy using a Sudoku app, isn’t there one available on more acceptable terms, e.g. a single purchase or a IAP that removes the ads from this one? I’m not saying you have to pay like $3.99/week for a scam one, but more like pointing out that if you don’t like ads (as I also don’t) why not support the developers who believe in selling software to you for a few bucks rather than selling your annoyance to Google via Adsense?