Make active group sync with slack

Right now poor evals has to update the @active group on slack which sounds unfun, and people could just automatically be added to that (and @meetings) when they're made on floor or hit the become active button. This means @active @frosh and @meetings could automatically be cleared when the new year button is hit as well

Locate the code handling floor creation, the “become active” action, the new year action, and existing Slack group updates. Trace how members are assigned to @active, @frosh, and @meetings, then verify that the requested additions and clearing behavior occur at each stated lifecycle event.

Written by the indexing model from the issue text.