I've since fiddled about with the "improved" interface to realize something, but first, for the benefit of those not able to understand how this came to be an issue for me (I am not alone in this, not by a long chalk; thousands of Steam users have multiple Steam account): While you SHOULD be able to catalog games by account and see the categories accurately delineate ownership...but the interface does not always behave the same from account to account.
The easiest way to avoid the issue is to be proactive, immediately move just-purchased games from Uncategorized to the appropriate category.
When you don't avoid the problem, when you initiate game installation you will be notified that you are borrowing—assuming you have granted library sharing rights across all of your accounts—such-and-such a game from such-and-such an account—when installation is attempted from an account other than that of the owner.
All change is not necessarily good or necessary, and the latest change to the Steam "browser" (not accurate nomenclature!) was neither beneficial nor needed. Library organization was far, far easier and accurate in the old interface...but neither do I entertain any absurd notions that there will ever be a "design rollback" just to make this cranky old man smile.