I think it would be great to see the saved searches as items in the sidebar.
I think this will be possible with this forthcoming feature: Ability to add a custom section of links to the sidebar
But would it support showing the number of new/unread etc? I think this requires some more logic than just saving a link.
Maybe not at first, but over time, I expect we’ll bake in some intelligence to particular kinds of links (which may be refined over time). For example, if we detect it’s a link to any kind of “topic list” then we could show an unread count for those.