So are you saying that if I install an app listed in the Installable Apps list from a repository, the App Manager will attempt to resolve dependencies automatically, even though it doesn't show that it's doing that? But if I install from a .deb file, the App Manager doesn't attempt to resolve dependencies from its repositories?

Why not? Why shouldn't those two situations be equivalent? If the .deb file shows that the app needs library X, and the App Manager has library X listed in one of its repositories, shouldn't it attempt to fetch it and install it? Still trying to understand how dependencies get resolved...