That's complicated because the Android and Apple app stores are run by different companies who have no incentive to cooperate. But some software stores do work

That's complicated because the Android and Apple app stores are run by different companies who have no incentive to cooperate. But some software stores do work this way. Steam for example. When you buy a game on Steam you are buying a license to all versions of the software -- you don't have a buy a Windows version, a Mac version, or a Linux version -- you get them all (if they exist). You even get versions that get released later. I've purchased games that only run on Windows and if they later get ported to Mac or Linux they show up in my library.