SessionManager.classifyNewTab's `initializing` branch relied on a
windowInitializing flag that start() cleared *before* the home tab's
chrome.tabs.onCreated event was dispatched (the event is asynchronous), so
the branch never ran in production and the home tab's classification was
subject to a timing race. Match the home tab by its tab id instead — the id
is already returned by ensureActiveTab and is reliable regardless of event
ordering.
Also refresh the overlay-bridge docstring: overlay.ready now makes the
background *push* the per-tab overlay state (and the Agent Window also
pushes on tab create / control-mode change), rather than a request/reply.
iAstro