I don't think that regular users helping in this forum ever use the Microsoft App store version, which is not the same as the Adobe one. It is customized to Microsoft's packaging requirements and sold and licensed from Microsoft directly.
So, you can't register it as if the software were the original Adobe version sold by Adobe or by resellers.
I don't know the exact advantages of the MS store, such as price and number of allowed licensed users. However the problems we see in this forum are diffictulties to get support and particularly updates. Installation procedures are different. The functions are nearly the same, so we can help for 'how to' questions, much less for debugging installation and updates issues.