That just shows me what other people see when they view my channel. It doesn't show me the unlisted/private videos, nor does it let me _manage_ them in any meaningful level.

Clicking on "Youtube Studio (beta)" will show me some videos with checkboxes, and let me do some editing, I think, which is probably the thing I'm usually looking for.

Nope. It only has your public videos -- no private, no unlisted.