Basically think of Home screens as an app and App Library as an app, they have different purposes and usage. The Home Screen allows user customisable folders and can now hide screens that are not used as much. The App Library is an App Store category based indexing system. You can't customise categories yourself in the App Store, same applies to App Library.
There is no point in having the App Library do what you want with folder naming, as that basically is just what the Home Screen is, and therefore makes it redundant.
App Library isn't for you, you'll never be happy with it, so therefore just don't use it and move on and use customisable Home Screen folders like you have been, as that's all you want.
I don't have any use for the Today screen, and I ignored it and wasn't bothered by it's existence ever since it was added to iOS.
That said, it would be great if we could turn it off....
To avoid swiping to it I found tapping the dots works well...