This experimental feature was discovered by some users, who found that when they try to take a screenshot of a tweet on the app, they get a prompt window that provides them with two alternative options for sharing the tweet. One is a Copy Link button, which allows them to simply copy the tweet link to their dashboard, and then share it anywhere they like.
The second one is a Share Tweet button, which provides a lot more options to share the tweet within the app itself. Whether it is through a DM, sharing to a specific community, bookmarking it for future sharing, or sending it through a message or chat application.
If you choose any of the following methods, you are still interacting within the Twitter ecosystem so that the app can count it as engagement. This, in turn, also gives them more opportunities to serve ads, as anyone who interacts with that link is essentially exposed to the app interface. If you simply screenshot the tweet, the app does not profit from any engagement that happens through your personal communications.
On the other hand, taking a screenshot is also a valuable activity, as you can now save that tweet for posterity, even if the original user deletes it because of some kind of backlash. At the same time, the tweet might be so offensive that you might want to provide it with any meaningful engagement, even if it happens through a simple share or retweet.
Moreover, the screenshot can be easily shared with people who don't even have a Twitter account, so they too, can take part in the conversation without having to install the app. So, it's not like the habit will suddenly die out just because Twitter is trying to discourage it with such a prompt. Let us wait and see if this remains a limited experiement, or if the platform turns it into a compulsory action.