How can I disable websites from being able to open App Store on iOS?
I use 1Blocker and Adamant content filters to block most JavaScript and trackers. That and careful decisions about what sites to visit have stopped this entirely from my iOS experience.

The ways that an advertiser can pay for placement means that some sites, you will never be able to get around this annoyance, but when it does happen, you can make note of that site abusing your time and at some point, you can stop visiting those sites where you are forced away from their content that you came to read in the first place.