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/archive/API_QUICK_REFERENCE.md

@@ -85,13 +85,53 @@ ws://localhost:5000/api/sessions/live
   }
 }
 
+// Vote received (live votes only, not chat-import)
+{
+  "type": "vote.received",
+  "timestamp": "2025-11-01T...",
+  "data": {
+    "sessionId": 123,
+    "game": { "id": 42, "title": "Quiplash 3", "pack_name": "Party Pack 7" },
+    "vote": { "username": "viewer123", "type": "up", "timestamp": "2025-11-01T20:30:00Z" },
+    "totals": { "upvotes": 14, "downvotes": 3, "popularity_score": 11 }
+  }
+}
+
 // Pong
 { "type": "pong" }
 ```
 
 ---
 
-## Live Voting
+## Votes
+
+### Get Vote History
+
+```http
+GET /api/votes?session_id=5&game_id=42&username=viewer123&vote_type=up&page=1&limit=50
+```
+
+**Response (200)**:
+```json
+{
+  "votes": [
+    {
+      "id": 891,
+      "session_id": 5,
+      "game_id": 42,
+      "game_title": "Quiplash 3",
+      "pack_name": "Party Pack 7",
+      "username": "viewer123",
+      "vote_type": "up",
+      "timestamp": "2025-11-01T20:30:00.000Z",
+      "created_at": "2025-11-01T20:30:01.000Z"
+    }
+  ],
+  "pagination": { "page": 1, "limit": 50, "total": 237, "total_pages": 5 }
+}
+```
+
+All query parameters are optional. No authentication required.
 
 ### Submit Live Vote