Fix review blockers in record chat

- Add Task.Supervisor to app supervision tree
- Use tagged tuples instead of rescue for error handling
- Pass embedding_text from parent LiveView as prop
- Remove dead Completion struct fields
- Extract socket assigns before Task closure
- Log errors server-side, show generic user message
- Make build_system_prompt private, remove thin wrapper
- Extract do_send_message for retry reuse

Co-Authored-By: Claude Opus 4.6 <noreply@anthropic.com>

lib/music_library_web/live/collection_live/show.html.heex

@@ -344,6 +344,7 @@
     sheet_id="record-chat-sheet"
     module={MusicLibraryWeb.Components.RecordChat}
     record={@record}
+    embedding_text={@embedding_text}
   />
 
   <.structured_modal

lib/music_library_web/live/wishlist_live/show.html.heex

@@ -308,6 +308,7 @@
     sheet_id="record-chat-sheet"
     module={MusicLibraryWeb.Components.RecordChat}
     record={@record}
+    embedding_text={nil}
   />
 
   <.structured_modal