I can see that a new object I'm making uses the Rug globals, for example. It's in the GLOB, and I cloned it from a rug, so no surprise, but how can I view what is inside a GLOB, what it's doing for the package? And how can I tell if an object is actually using it?

Look in the Object Functions (OBJF), rugs in particular don't usually have any behaves but use the semi-globals as defined in the GLOB. Items that have a GLOB can use the semi-globals for constants, pie menus, behaves, text lists etc. and removing it normally requires adding a lot more resources from the semi-globals than you could save by removing it.

To view what's actually in the semi-globals the GLOB will show the semi-global group as Group:, you'll need to open the objects.package to that group.

There's another way if you want to see only a specific BHAV semi global.
When you're viewing your BHAV, click on the node that is gloal (2000 & further). Then on the right side, you'll see the opcode of this BHAV Global, click on the "view BHAV" (it will open the BHAV)