After I installed Windows 11 on my Surface Pro 3 I did exactly that. I went to the App Store, tapped GET and nothing. I once more searched the Internet, nothing that worked. Then I figured it out. Like Android Microsoft limits the number of registered devices to a Microsoft or Windows account. The maximum number of devices according to Microsoft is 10, however in may case it tops out at 5, a 6th device can't make use of the store. I logged into my Windows account using a browser and navigated to my devices and removed the redundant ones, the App Store worked fine.
This has long been a curse of the Windows App Store and not even Microsoft is fully aware of the problem and the fix, they have never posted it and if you go to their forums you will not find this suggestion from Microsoft at the time of this post.
In reply to another reader I emailed Maximum PC magazine with the fix and they published it in the August 2021 issue. I have posted a shot of it as well. I know that many will now start to post this fix in self help forums and many will also take credit. However the article is published and dated. So please when posting the fix be honest where it came from.