Authorization vs. association
Up to 5 computers can be simultaneously authorized for each Apple ID. There is no direct record of which machines are authorized. It is up to you to keep track. (I use a small text file in my main iTunes folder.) iPods & iOS devices are limited to DRM protected content from up to 5 different accounts. There is no limit to the number of devices that you can load up with content using iTunes, or the number of Apple IDs a computer can be authorized to. You can deauthorize computers that you no longer wish to use to access protected content so that you can authorize others. You either do this on the specific machine or deauthorize all and then reauthorize as needed. Having used deathorize all you cannot use it again for a year, though Apple Support may be able to perform a reset if you can explain why you need to reuse the feature before it becomes available to you. Reinstalling Windows without deauthorizing first will use up an authorization.
A mix of up to 10 computers and iOS devices (no more than 5 computers) can be associated with your Apple ID for iTunes Match/Apple Music, automatic downloads, or redownloads of past purchases. There is a 90 day limit before a computer or device can be switched to another ID or the association removed. The list of associated devices is the one you can see within your account details in iTunes or Music. Association doesn't apply to HomePods or Apple TVs. You associate a device or computer by using certain features, such as downloading past purchases. You don't necessarily need to associate a computer or device with your Apple ID to use it with your content if you can copy the content from another computer. Again Apple Support may be able to reset if you can explain why you need to reset the association early. Note that each country's store is a separate entity in this respect which adds another complication to changing your Apple Account country or region - Apple Support.
You can remove any and all associations that are not within the 90 day limit. Those that you actually use will be recreated as and when you make use of a service that triggers association. If you've used multiple Apple IDs you should settle on one primary ID to use in future. This would typically be the one used to purchase apps as they will need updating using the ID that purchased them. Download all other content when you are able to. It may be possible to Set up Family Sharing - Apple Support to allow your main ID to access past purchases from your other IDs.
iCloud Music Library
Although iTunes can sync content from a number of accounts to a device iCloud Music Library, which comes with the Apple Music or iTunes Match services, will treat any purchased media from a different account as ineligible. A workaround is to convert such tracks to fresh 256k AAC copies then archive your originals to clean up the library so it only contains the working copies that can sync to your devices.
Corrupt downloads
Repeated requests to authorize an already authorized computer for recent store downloads typically indicates you have corrupt or incomplete copies. Delete the tracks that won't play from your library without hiding from your purchase history. Redownload using the cloud links that should remain, or close the application and reopen if they don't show up straight away. While downloading click the activity widget and turn off the option that allows for simultaneous downloads.
If that hasn't helped see If iTunes prompts you to authorize your computer when you try to play iTunes Store purchases - Apple Support.
Where am I signed in?
There is another list of devices and browsers that you may have signed into with your Apple ID. See Check your Apple Account device list to find where you’re signed in - Apple Support for more on this list, which is separate from the lists of authorized and associated devices. Note that it is sometimes possible for the same device to be listed more than once, likely due to signing into your Apple ID in a browser which would be treated separately from iTunes.