Have you cleared the cache from the keyboard? To do this follow the path from my screenshots, go to settings, apps, type in the search box Samsung Keyboard, open it to get to the app info page, go to storage and clear cache.
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You are correct; screenshots are handled by the OS, and apps block them. Neither Google, Apple, nor Samsung, with their UI skin over Google's Android platform, are going to override what an app will allow for, FULL STOP! You haven't explained a scenario in which you need this to be a thing. If it is that important, just take a photo of the screen with another device; problem solved.
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App developers are just that developers. They can do whatever they want with their apps as they see fit. Samsung is not going to override what an app can and cannot do because you want them to.
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In a future update to Google Messages you will be able to @ someone in a Group text to ensure only that individual or multiples get the photos and videos in a group chat.
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