Generate a design from a plain-English brief

Scope: ai. Decrements the monthly synthesis counter (Pro 5, Team 15; an account with its own AI key is not metered). At most 5 calls an hour per account through the API, across all its keys (429 RATE_LIMITED). At most 3 syntheses run at once per account on the server that takes the request, the editor's included; a 4th is 429 SOLVE_IN_PROGRESS with Retry-After: 30 and does not count against the hourly limit. Returns the generated design, already solved, with the same disclaimer the editor shows. Pro and Team only: a Free account is refused with 403 PLAN_REQUIRED (one sentence and the trial link).