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/open_ai/completion.ex

@@ -3,7 +3,5 @@ defmodule OpenAI.Completion do
   defstruct content: "",
             temperature: 0.2,
             role: "user",
-            model: "gpt-4o-mini",
-            messages: nil,
-            response_format: nil
+            model: "gpt-4o-mini"
 end