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

docs/api/README.md

@@ -40,6 +40,8 @@ All REST endpoints are prefixed with `/api/` except `/health`.
 - `GET /api/sessions/active`
 - `GET /api/sessions/{id}`
 - `GET /api/sessions/{id}/games`
+- `GET /api/sessions/{id}/votes`
+- `GET /api/votes`
 - `GET /api/stats`
 - `POST /api/pick`
 - `GET /health`
@@ -82,7 +84,7 @@ SQLite stores booleans as integers (0/1). In request bodies, pass JavaScript boo
 
 ## Pagination
 
-No pagination. All list endpoints return full result sets.
+Most list endpoints return full result sets. The exception is `GET /api/votes`, which supports pagination via `page` and `limit` query parameters (default: page 1, limit 50, max 100).
 
 ## Quick Reference
 
@@ -128,6 +130,7 @@ No pagination. All list endpoints return full result sets.
 | DELETE | `/api/sessions/{id}` | Yes | Delete a session |
 | POST | `/api/sessions/{id}/close` | Yes | Close a session |
 | GET | `/api/sessions/{id}/games` | No | List games in a session |
+| GET | `/api/sessions/{id}/votes` | No | Get per-game vote breakdown for a session |
 | POST | `/api/sessions/{id}/games` | Yes | Add a game to a session |
 | POST | `/api/sessions/{id}/chat-import` | Yes | Import chat log for vote processing |
 | GET | `/api/sessions/{id}/export` | Yes | Export session |
@@ -154,6 +157,7 @@ No pagination. All list endpoints return full result sets.
 
 | Method | Path | Auth | Description |
 |--------|------|------|-------------|
+| GET | `/api/votes` | No | Paginated vote history with filtering |
 | POST | `/api/votes/live` | Yes | Record a live vote (up/down) |
 
 ### Webhooks