fix(app-state): actually send the coalesced broadcast

[alpha5611331]

Closes #81.

The main process never delivered a single app:state-updated push to the renderer, so the renderer ran forever on the one snapshot it took when the first component mounted. Reported as "the Start button does nothing"; a fresh login was equally dead.

Root cause

this.broadcastTimer = setTimeout(() => {
  this.broadcastTimer = null;   // handle cleared here...
  this.flushRenderer();         // ...so flushRenderer's own guard trips
}, BROADCAST_COALESCE_MS);

flushRenderer() opens with if (!this.broadcastTimer) return; and holds the only webContents.send('app:state-updated', ...) in src/main/. Nothing outside test/ calls it. So every real broadcast went through the timer path, and the timer path sent nothing.

The renderer never recovers because use-app-state.tsx starts its polling fallback only when onAppStateUpdated is absent. It is present, so the renderer subscribed to a channel that never fired and never polled.

Change

Extract the send into private sendToRenderer(). The timer callback calls it directly; flushRenderer() keeps its pending check - which is its documented contract, and what the identical updates do not broadcast check relies on - then calls it. No signature or semantic change to flushRenderer().

Test

Every existing check in test/app-state.test.mjs calls flushRenderer() synchronously while the timer is still pending. That is the one arrangement in which the send worked, which is exactly why this shipped green. Added a check that lets the timer fire on its own with no flush at all.

Verified red before the fix and green after (rebuilding electron-dist/ in between - node test/run.mjs alone runs stale output):

  FAIL a coalesced broadcast reaches the renderer
  FAIL the coalesced broadcast carries the change

pnpm test:main, pnpm lint, and pnpm build all pass on the branch.

What this unblocks

Every consumer of the push channel, not just Start: fresh login navigation, the isLoggedIn: null startup window that could pin MainPage on "Authenticating…" forever, Idle -> Starting -> Running button transitions and TransitionOverlay, live transcripts and both suggestion panels (stuck on placeholder content for a whole interview), credits / user role / backend-live indicators, and the Clear reset from 3a7b660 whose broadcast could not send.

Also audited

Same class of defect across the client, all clear: every ipcMain channel has a matching preload binding and vice versa; all push channels main sends have live preload listeners; the timers in action-lock.service.ts and the stall timers in both suggestion services are correct - none repeats the clear-then-call-a-guarded-method shape.

Two pre-existing items noted in #81 as out of scope: the audioInputDeviceNotFound use-before-declaration in control-panel/index.tsx, and enumerateDevices() returning blank labels before mic permission is granted.

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