Reader: Only show sites with unseen items in the sidebar

It would be really nice to only show sites with unseen items in the expanded reader sidebar. I follow over 1000 sites and limiting it to stuff with items to read would be very handy.

Ties in with https://github.com/Automattic/wp-calypso/issues/43592 a bit

Start by tracing the Reader's expanded sidebar and how it receives or determines unseen items. Review the related issue #43592 for context, then verify that the expanded sidebar shows only sites with unseen items while retaining the expected behavior for sites without them.

Written by the indexing model from the issue text.