Research: what social media info could go in site status aka "Kate's Action Area"

Time Box this to a few hours of pinging and getting answers.

We think it would be interesting to inform the user of the status of their social media connections in wp.com. For example, if the user has connected their social media account we might prompt them about
* disconnection problems
* # times their post or site is shared on social media

We are looking for a really quick win, an api that is readily available or data readily available that we can use in the site status area.

Related
pd2qGl-9y-p2#site-status
[Site Status idea spreadsheet](https://docs.google.com/spreadsheets/d/1irL6xZnAPMOVl-p3YGUYkn2mbjlD8r2uV8SEhcU0jl8/edit#gid=0)

Start with the site status area and the related site status idea spreadsheet. Investigate whether readily available APIs or data can show social connection problems or sharing counts, and document the promising options. Done means a brief feasibility recommendation identifying a quick win or confirming that none is available.

Written by the indexing model from the issue text.