refactor(web): dock chat inline below the summary, integrated view (ADR-027)

The chat was a separate page — opening it left the summary behind, the very
context you're asking about. Now the chat docks open IN PLACE below the summary:
"Dig deeper" reveals the chat section (HTMX, outerHTML over the closed dock) so
the summary stays on screen above it; no navigation. The no-JS fallback renders
the full summary AND the open chat on one page (the same integrated view), so
progressive enhancement holds.

Extracts a shared summaryBody templ so the detail page and the chat page render
one identical summary, not two divergent ones. GET /v/{id}/chat returns just the
open chat section as a fragment for the inline reveal, or the full summary+chat
page for a no-JS navigation; POST swaps the panel inline or re-renders the whole
page. Tests assert summary+chat coexist on the page and the reveal is a fragment.

Co-Authored-By: Claude Opus 4.8 (1M context) <noreply@anthropic.com>

docs/use-cases/chat_transcript.feature

@@ -14,6 +14,12 @@ Feature: Chat with a video's stored transcript
   Scenario: A summary view offers a deeper-dive into the video
     When I view the summary
     Then I see a "dig deeper" affordance that opens a chat about this video
+    And it opens the chat in place, below the summary, without leaving the page
+
+  Scenario: The summary and the chat are on one page
+    When I open the chat
+    Then the summary stays visible alongside the chat
+    And I can read the summary while I ask questions
 
   Scenario: Ask a question answered from the stored transcript
     When I ask a question in the chat