feat: add WebVTT context generation to chat WebSocket endpoint

- Import topics_to_webvtt_named and recordings controller
- Add _get_is_multitrack helper function
- Generate WebVTT context on WebSocket connection
- Add get_context message type to retrieve WebVTT
- Maintain backward compatibility with echo for other messages
- Add test fixture and test for WebVTT context generation

Implements task fn-1.2: WebVTT context generation for transcript chat

.flow/specs/fn-1.3.md

@@ -0,0 +1,67 @@
+# Task 3: LLM Streaming Integration
+
+**File:** `server/reflector/views/transcripts_chat.py` (modify)
+**Lines:** ~35
+**Dependencies:** Task 2
+
+## Objective
+Integrate LLM streaming with conversation management.
+
+## Implementation
+```python
+from llama_index.core import Settings
+from reflector.llm import LLM
+from reflector.settings import settings
+
+# After WebVTT generation:
+# Configure LLM
+llm = LLM(settings=settings, temperature=0.7)
+
+# System message
+system_msg = f"""You are analyzing this meeting transcript (WebVTT):
+
+{webvtt_truncated}
+
+Answer questions about content, speakers, timeline. Include timestamps when relevant."""
+
+# Conversation history
+conversation_history = [{"role": "system", "content": system_msg}]
+
+# Replace echo loop with:
+try:
+    while True:
+        data = await websocket.receive_json()
+        if data["type"] != "message":
+            continue
+
+        # Add user message
+        user_msg = {"role": "user", "content": data["text"]}
+        conversation_history.append(user_msg)
+
+        # Stream LLM response
+        assistant_msg = ""
+        async for chunk in Settings.llm.astream_chat(conversation_history):
+            token = chunk.delta
+            await websocket.send_json({"type": "token", "text": token})
+            assistant_msg += token
+
+        # Save assistant response
+        conversation_history.append({"role": "assistant", "content": assistant_msg})
+        await websocket.send_json({"type": "done"})
+
+except WebSocketDisconnect:
+    pass
+except Exception as e:
+    await websocket.send_json({"type": "error", "message": str(e)})
+```
+
+## Validation
+- [ ] LLM responds to user messages
+- [ ] Tokens stream incrementally
+- [ ] Conversation history maintained
+- [ ] `done` message sent after completion
+- [ ] Errors caught and sent to client
+
+## Notes
+- Test with: "What was discussed?"
+- Verify timestamps appear in responses