Generate All Schedules

Start one background task to generate all remaining schedules up to the limit.

Args: schedule_id: Unique identifier of the generation session to exhaust.

Returns: Confirmation containing the current retained count and target limit; the response does not wait for enumeration to finish.

Raises: HTTPException: Status 404 for an unknown session, 409 when another background run is active, 400 when the requested limit is already reached, or the initialization errors documented by the scheduler/generator helpers.

Behavior: Initialization completes before a single session-owned task is created. That task repeatedly uses the same locked advance path as /next, stopping on the requested bound, solution-space exhaustion, cancellation, or error. Terminal reasons and unexpected error text are recorded for status queries; concurrent next or generate-all calls observe the active-task conflict.

GenerateAllResponse(message='...', current_count=1, target_count=10)