feat(public): venue/projector mode for public competitions (#77)

[tbcsec]

What & why

Closes #77. A full-screen, unauthenticated venue/projector mode for putting a live competition on the big screen at an in-person event. It's an in-page toggle on the existing /public/[id] spectator view (?venue=1, bookmarkable and refresh-safe) and implied by the same public_scoreboard opt-in — no new competition column, permission, event, or WebSocket.

The stage auto-rotates three widgets — scoreboard, insights (stats + highlights), points timeline — at 15s each (?interval= override), with a first-blood takeover overlay using the app's house amber-lightning glyph. Operator controls: a fullscreen button, arrow keys to step, space to pause, Esc to exit.

Decisions (confirmed with the owner)

• In-page toggle, not a separate route — but URL-addressable via ?venue=1 so it's still castable/bookmarkable.
• Widgets: scoreboard, insights, timeline. The live-solve ticker was cut, but first-blood splashes stay — so the feed below still exists, used solely to drive the splash.
• Polling, no WebSocket (per the sizing answer) → no ADR needed; reuses the established public-endpoint pattern exactly.
• Auto-rotate + fullscreen button, keyboard as a bonus. Fixed 15s + ?interval= override.
• First-blood mark reuses the existing lightning FirstBloodIcon, not a droplet — consistent with the rest of the app.

Backend — one read-only endpoint

• GET /api/public/competitions/{id}/activity → recent awarded solves, each tagged is_first_blood. Freeze-aware (computed as of freeze_cutoff), so a frozen competition emits no post-cutoff solves — the splash goes silent during a freeze rather than leaking hidden movement. Same opt-in/archived 404 gating as the board; short in-process memo (public_activity_cache_seconds, 5s).
• First-blood detection refactored into one shared _first_solvers helper so the feed and the insights leaderboard can't disagree.

Frontend

• ?venue=1 toggle on the spectator page (Suspense-wrapped useSearchParams); usePublicActivity polls only while venue mode is on.
• components/public/venue/venue-mode.tsx — the overlay: rotation, first-blood splash queue (primed on first load so pre-existing bloods don't storm), fullscreen + keyboard controls.
• Extracted StatTiles/Highlights (shared with the static page, no fork) and the FirstBloodIcon (shared with the challenges page).
• Pure helpers in lib/venue.ts (parseRotateSeconds, pickNewFirstBloods) — unit-tested.

Verification

• Full gauntlet green: backend pytest 641, frontend tsc / eslint / vitest (197, incl. 17 new) / next build.
• Freeze-parity test proven load-bearing (neutered the cutoff → the security test fails).
• Two adversarial reviews (correctness + conventions) — no bugs; one letter-spacing token nit found and fixed.
• Live-verified against a demo-seeded instance: entered venue mode, rotated through the scoreboard and timeline slides, confirmed the freeze-aware /activity feed and zero console errors.

Checklist

• Follows the architectural rules in CONTRIBUTING.md (Pydantic schemas separate from models, one router/hook per domain, design tokens, read-only public route needs no event/permission, a11y role=tablist/aria-pressed/role=alert)
• N/A — no schema/migration change
• This is not a security fix (but the new endpoint is unauthenticated public surface, reviewed as such: freeze-aware + opt-in gated)

🤖 Generated with Claude Code