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-1.7.md

@@ -0,0 +1,54 @@
+# Task 7: Integrate into Transcript Page
+
+**File:** `www/app/(app)/transcripts/[transcriptId]/page.tsx` (modify)
+**Lines:** ~15
+**Dependencies:** Task 5, Task 6
+
+## Objective
+Add chat components to transcript detail page.
+
+## Implementation
+```typescript
+// Add imports
+import { useDisclosure } from "@chakra-ui/react"
+import {
+  TranscriptChatModal,
+  TranscriptChatButton,
+} from "../TranscriptChatModal"
+import { useTranscriptChat } from "../useTranscriptChat"
+
+// Inside component:
+export default function TranscriptDetails(details: TranscriptDetails) {
+  const params = use(details.params)
+  const transcriptId = params.transcriptId
+
+  // Add chat state
+  const { open, onOpen, onClose } = useDisclosure()
+  const chat = useTranscriptChat(transcriptId)
+
+  return (
+    <>
+      {/* Existing Grid with transcript content */}
+      <Grid templateColumns="1fr" templateRows="auto minmax(0, 1fr)" /* ... */>
+        {/* ... existing content ... */}
+      </Grid>
+
+      {/* Chat interface */}
+      <TranscriptChatModal open={open} onClose={onClose} {...chat} />
+      <TranscriptChatButton onClick={onOpen} />
+    </>
+  )
+}
+```
+
+## Validation
+- [ ] Button appears on transcript page
+- [ ] Clicking button opens dialog
+- [ ] Chat works end-to-end
+- [ ] Dialog closes properly
+- [ ] No layout conflicts with existing UI
+- [ ] Button doesn't overlap other elements
+
+## Notes
+- Test on different transcript pages
+- Verify z-index for button and dialog