docs: update remaining docs with vote tracking API changes

Update README.md, docs/api/README.md, session-lifecycle guide,
webhooks-and-events guide, and archive docs (BOT_INTEGRATION,
API_QUICK_REFERENCE) with new endpoints and vote.received event.

Made-with: Cursor

README.md

@@ -36,6 +36,8 @@ A full-stack web application that helps groups pick games to play from various J
 
 - **Live Voting API**: Real-time vote processing from external bots
   - Accept live votes via REST API
+  - Real-time `vote.received` WebSocket event for stream overlays
+  - Per-session vote breakdown and paginated global vote history
   - Automatic deduplication (1-second window)
   - Timestamp-based game matching
   - JWT authentication for security
@@ -249,6 +251,7 @@ The manifest is automatically generated during the build process, so you don't n
 - `POST /api/sessions` - Create new session (admin)
 - `POST /api/sessions/:id/close` - Close session (admin)
 - `GET /api/sessions/:id/games` - Get games in session
+- `GET /api/sessions/:id/votes` - Get per-game vote breakdown for a session
 - `POST /api/sessions/:id/games` - Add game to session (admin)
 - `POST /api/sessions/:id/chat-import` - Import chat log (admin)
 
@@ -258,7 +261,8 @@ The manifest is automatically generated during the build process, so you don't n
 ### Statistics
 - `GET /api/stats` - Get overall statistics
 
-### Live Votes
+### Votes
+- `GET /api/votes` - Paginated vote history with filtering
 - `POST /api/votes/live` - Submit real-time vote (admin)
 
 ### Webhooks