This could be related to two factor and/or two step authorization, so be sure to log in to you AppleID from Safari and or another browser to check your password and account status for any locks.
At a high level, the App Store is a global network of load balancers that provide listings to make up the content you see in the App Store. It has a second level of load balancers that handle the transition to "buy" anything and once that transaction happens, then your account will go initiate the request to download a purchased asset.
Lots of things can go wrong and usually it's with the network or one of the servers behind the load balancer that's stuck and the load balancer doesn't know that it's broken and route around that one failure on one server.
Practically, you can and should wait as a first step. Log out, restart the Mac, get some tea or coffee and try again. When you have a persistent failure, then here's how I attack it.
- Verify that the purchase was made by reloading the App Store purchased tab and verifying the item cleared the purchase and was assigned to my Apple ID.
- Verify you can download anything you purchased in the past.
- Retry the item you wanted.
By knowing if it's an issue with allocating that item to your account, you can do very little except sign out, sign in, try another account on your Mac or another Mac and then contact store support for purchasing support.
If you can purchase the item but can't download it or the other one - now you're back to figuring out the network of content delivery servers.
Also, the App Store can tell you if it's working well if you look at an app you have a backup or can afford to re-download once your account is set. Find that app in purchased and move it to trash. The App Store should change from telling you it can open that app to it can download that app pithing a few seconds of moving that app to Trash. If you attempt to re-download it, the console app will log hundreds of diagnostic messages to the logs.
As long as you see TLS Events you'll know that secure communications from your App Store App to Apple's load balancers is being attempted.