Extract orchestrator inner loop into _doOrchestrate() so the retry button
can re-run without re-adding the user message to DOM or history — same
pattern as the existing chat retry.
Also set AsyncOpenAI(timeout=settings.timeout_local) so slow remote models
(OpenRouter/DeepSeek) get the same 300s budget as local chat calls instead
of the SDK default which varies by connection.
Co-Authored-By: Claude Sonnet 4.6 <noreply@anthropic.com>