Add releases to doc status badges

[stevenle]

Description

The "draft/published" states in the doc status badges should also include a list of the "pending" releases the doc is in.

Implementation note: to avoid having to repeatedly query the backend for this info, maybe we should set up a context provider that stores global state and is connected to the firestore callback system. This allows us to generally store state at the app level without having to repeatedly make RPCs to firestore.