Open-questions nav badge (live counter via broadcast) + whole-site ding on new open question

DONE — built on branch `flower/109-open-questions-badge` (off master), commit 725dbc0. NOT merged/pushed. Reused the #75 roster Reverb/Echo pattern (dedicated ShouldBroadcast event + private channel + Echo listener). (a) NAV BADGE (bloom): accent count pill on the left-nav "Briefs" link showing the number of OPEN brief questions (resources/views/components/layouts/app.blade.php). Always in the DOM (hidden at 0) so a 0→N broadcast reveals it without a reload. Count = new `App\Models\BriefQuestion::openCount()` — single source of truth shared by the badge, the broadcast payload, and tests. (b) LIVE UPDATE: new `App\Events\OpenQuestionsChanged` (ShouldBroadcast) on a new private channel `open-questions` (routes/channels.php), payload {open_count, created}. BriefService dispatches it AFTER commit from askQuestions (created: true) and answerQuestion (created: false), so the count reflects committed state. Best-effort like DaemonCheckedIn — a broadcast failure never fails the write. NOTE: there is no brief_dismiss path in the app today (only ask + answer change the open count), so dismiss isn't wired; answer covers the decrement case. (c) WHOLE-SITE DING: one global Echo subscription in resources/js/app.js (window.Echo persists across Livewire wire:navigate, so it covers every page) updates the badge in place and plays a subtle two-note WebAudio chime — ONLY on `created` (new open question), never on answer. Honors a `flower-oq-muted` localStorage flag so a future mute toggle can silence it (UI toggle not built — nice-to-have). JS / ASSET CHANGES (important — run npm run build on MAIN at merge): - resources/js/app.js WAS EDITED (added the global Echo subscription + badge updater + WebAudio ding). The compiled bundle must be rebuilt: `npm run build` on MAIN so the change ships. Reverb is on 8090 (VITE_REVERB_* already configured). - NO binary audio asset was added — the ding is generated via WebAudio (same approach as the existing operator-feed bell), so there's nothing new to bundle beyond the JS. - Autoplay caveat: browsers may defer the first ding until the operator has interacted with the page; the ding is an enhancement, so acceptable. Kept bloom, no FluxUI. Verify on flower.test: badge count + live update + ding on a real brief_ask. Tests: new tests/Feature/Briefs/OpenQuestionsBadgeTest.php (openCount counts only open; ask broadcasts created=true + right count; answer broadcasts created=false + decremented; empty ask doesn't broadcast; nav badge renders the live count). Test result: `MEILISEARCH_KEY=LARAVEL-HERD ~/bin/php artisan test` → 688 tests, 687 passed, 1 skipped (pre-existing), 0 failures. `~/bin/php ./vendor/bin/pint --dirty` → passed. app.js syntax validated via node --check.

Operator (2026-07-03): make open brief questions impossible to miss. ## Items 1. **Nav badge + counter:** in the left nav under "Briefs", a badge showing the live COUNT of OPEN brief questions (brief_questions where status=open, in the operator's scope). 2. **Live update via broadcast:** when an open question is created (brief_ask) — or answered/dismissed, changing the count — broadcast a Reverb event and update the nav badge WITHOUT a page reload. Reuse the existing Reverb/Echo infra: flower runs Reverb on 8090, and Brief #75 added roster live-updates-on-check-in — follow that same pattern (event + channel + JS/Echo listener). 3. **Whole-site ding:** a subtle site-wide audio bell when a NEW open question is CREATED (brief_ask), played globally on any page so the operator is alerted immediately. Add a small audio asset + a global Echo listener that plays it. Ding ONLY on new-open-question creation (not on answer/dismiss). Tasteful/subtle; a mute toggle is a nice-to-have. ## Touch points - Nav/layout component (the badge) — likely resources/views/components/layouts/* + the nav partial. - A broadcast event fired where open questions are created/changed: the brief_ask path (BriefService / the MCP brief_ask + brief_answer/brief_dismiss for count deltas). - A global Echo channel subscription + JS handler + audio asset (app.js / layout script). ## Notes - FluxUI (#105) is landing — the badge MAY use a Flux badge once available, but do NOT block on it; the broadcast + audio is the substance. - bloom styling; keep `php artisan test` green; `./vendor/bin/pint`; verify on flower.test (badge count updates + ding fires on a real brief_ask). Commit trailer `Brief: #<this-id>`.