Who's in charge of deploying docrails changes to the live site? Seems
like people are contributing a lot to docrails but the site is rarely
updated. When was the last time everything was deployed live and how
often is it redeployed?

The official Rails documentation is part of Rails releases. Thus, when
a stable release is out, the stable docs are generated and published.
API and guides. That process is nowadays automated and is rumored to
be as robust as to be able to handle a nuclear war, but me myself
tries to be around just in case :).

On the other hand, every push to master triggers regeneration of the
edge docs right away there's a webhook for that.

Note that in particular docrails is never published. All docs, stable
or edge, are published from the stable tag or master. Because the
rails repository is the one that hosts the project itself, its code,
its tests, and its docs.

Nowadays I am the one who cross-merges master and docrails, weekly or so.