That's a really good question. Every app, including ThreadBook, has its own chunk of iCloud space. However the space used by ThreadBook is a special allotment that is available to all devices using the same Apple ID, even if they have never logged in to iCloud. It is limited to 1MB, so it uses very little of the 5GB you get for free. I chose to use this because not all users of iPads are aware of iCloud or how it works. Because of the very limited size of this space, most apps use the conventional iCloud storage that requires you to log in. There are three different types of storage available to each app. The PUBLIC storage is where the app developer usually stores things that are common to all installed apps. This would be things like images for game levels, templates, and in the case of ThreadBook, updates to the Library installed on each device. Because this space is public, it does not count against your storage. It's generally free to the developer, although there is a formula that Apple uses to charge for it depending on the amount of storage used, the number of app installations, and the amount of bandwidth used. PRIVATE storage is where the documents live that you create, like text documents, spreadsheets, etc. This space does count against your allotted storage. The third type of iCloud storage is SHARED. This is where things go that app users want to share with other users. It might be things like photos, calendars, or other items of interest to a particular group. This also does not count against your allotted iCloud storage.
Initially apps could only open files in their own iCloud space, whether PUBLIC or PRIVATE. That fits the model that most people have of how computer storage works. Many times in helping my beloved with document issues, I would say where did you save it and I would get the answer "Word". Because the document was created by Word, it was assumed that's where it would be, and I would respond with "Word is a program, not a place." However in the first generation of iCloud, each app was also a place. This created frustration if you wanted to open a document, such as a plain text file, with a different app than the one that created it. Apple modified iOS so that a file could be copied from one app's space to another. This capability is still there today, as we saw in previous posts about opening embroidery files in AcuEdit. They then opened things up even more by allowing an app to open a file in another app's space if you have permission. This allows, for example, for multiple people to edit the same document. It's a little tricky to program for, and is not generally used outside of the Apple "business" apps like Pages, Numbers, and Keynote. In a recent iteration of iOS they introduced the "Files" app, which essentially lets you browse all of your iCloud files like you would on a desktop or laptop computer. Like Windows, when you open a file it will open in the app the is assigned to open such files. Also like Windows, having one and only one app to open a file of a given type creates problems. With that app you also get iCloud Drive, which is basically a storage bucket that you can reach from your iPhone, iPad, Mac, or Windows PC. This makes for convenient backup, but it's not at all clear how you can manage it. As you discovered, "Manage Cloud Storage" is an all-or-nothing proposition and not at all what the name would imply.
The most recent iOS version, 13, seems to be proof that 13 is an unlucky number due to the large number of bugs and frantic updates it has had. However it does have one feature that makes it easy to manage files. Whether you are looking at document in an app (Note - a document could be a spreadsheet, a text document, image, or whatever the app is built to make), or a document in the Files app "Browse" function, tapping and holding the document will produce a menu of options. This includes Copy, Duplicate, Move, *AND* Delete. Be very careful with the delete option, as it does not ask you to confirm. It just deletes, immediately. If you navigate back to the first page of the Browse function you will find a folder of "Recently Deleted" files. Tap and hold on a document there to Delete Now (forever!) or Recover. You can also tap the "Info" button to get more details about the file.
When you buy any Apple device you get 5GB of iCloud space for free. That's NOT 5GB per device, it's just 5GB period. This is pretty meager, especially if you let Apple store all your photos in iCloud, which they will do by default if you don't stop them. You can get 200GB of storage for $3 a month, and you can share that with other family members. The next jump is 2TB (2,000GB) for $10 a month. There are no other options. A number of other companies offer cloud storage, one example being Dropbox. However all of them will reach a point where you have to pay, and none of them are as smoothly integrated into iOS as iCloud.
Hopefully this clarifies things a bit, but please feel free to follow up with additional questions. Since creating ThreadBook I have, of necessity, had to learn a lot more about iCloud.