Truncated responses are detected and handled gracefully

When finish_reason: "length" fires and the application ignores it, users receive half-written code, truncated JSON that fails to parse, or advice that ends mid-clause — and they have no signal that anything was cut. They act on incomplete information, file bug reports against the wrong component, or lose trust in the assistant entirely. The error-resilience taxon requires surfacing partial-output states; silent truncation is the worst possible UX for a recoverable failure because it looks like a complete answer.

After every non-streaming API call, inspect finish_reason (OpenAI) or stop_reason (Anthropic) and propagate a truncation flag to the UI so the user sees a "Response may be incomplete" banner with a continue button. Wire this through api/chat/route.ts.

const choice = response.choices[0]
return { content: choice.message.content, truncated: choice.finish_reason === 'length' }