Afraid, can buy the same albums twice or more

Did you buy them with the Apple ID you are currently using?

If so, try following the steps here to find and download them: Redownload apps, music, movies, TV shows, and books from the App Store, iTunes Store, and Apple Books - Apple Support

Sometimes rights holders modify the songs or albums, and may appear as not being bought if they are set as new items rater than updates to the originals. In many cases, your purchases can still be found in your Purchase history, rather than directly in the iTunes store, and can be re-downloaded from the purchase history list.

Clearly there is no good reason for you to buy the same content if you already have it, but as you have found out relying on the iTunes Store to know what it is in your library isn't a sufficient check. I meant to mention that content can be withdrawn from the store, then later put back as new content which won't necessarily match up with a previous purchase. This might happen, for example, if the distribution rights for digital content in a particular region change hands. The terms of use of the iTunes Store make it clear that the ability to redownload purchased content relies on its continued availability in the store. If you've lost content in this way you can see if iTunes - Official Apple Support are able to attach the new versions to your account, but I would doubt it.

tt2

Does it say Purchased, or show the price? If it says Purchased then the items are hidden in your purchase history, and you should be prevented from an accidental repurchase. Unhide them to get an option to redownload. Any content in the iTunes Store is only there as long as the rights holders wish it to be. Should they remove it for any reason, bang goes your ability to redownload. You should always keep local copies and backups, or accept the risk. All my music is downloaded. I leave my iTunes video purchases in the cloud knowing there is a small but real risk that I might lose access to one or more of them at some point down the road and console myself with the thought that, should it happen, those will on Netflix or Prime by that point.

tt2

As the previous respondents have said it happens a lot more than you'd realize. It gets especially confusing when you have access to Applemusic, do yourself a favor if you don't remember music you already bought take the extra time to check because I can assure you that even when you contact support they won't see that as a reason to issue you a refund.

Glad it worked out.