The original Stack Exchange app has this cool feature where you can browse hot question from the entire network.
But at the current state I am not able to see a “Stack Exchange” site listed in the websites API (I can only see “Meta Stack Exchange”).
Am I missing something? Are you going to implement it?
You are not missing something.
'Stack Exchange' is not a site in terms of Questions and Answers. It has the sole purpose of offering users (not API consumers) a common place across all network sites. That is why your network account is there for example, among some other network generic features like Hot Questions and a real-time feed. Further more it offers navigation to informational pages solely catered by Stack Exchange, Inc.
There are a few undocumented (and some can change / be sunsetted at will) features to make sense for automated consumption. I'll list and link to their canonical posts here:
There also is/was mobile.stackexchange.com but that gets decommissioned so I only mention it for historic reasons.
