Get Next Schedule

Generate, retain, and return exactly one next schedule for a session.

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

Returns: The newly generated schedule, its zero-based index, and total retained count.

Raises: HTTPException: Status 404 for an unknown session, 409 while generate-all is active, 400 at requested-limit or solution-space exhaustion, 408/422 for initialization problems, or 500 for unexpected generation failures.

Behavior: Background conflicts are checked both before and after lazy scheduler and generator initialization. The shared advance path holds the session lock, calls next on the Z3 executor, appends serialized and original forms atomically, blocks duplicate models through the generator, and refreshes TTL.

ScheduleResponse(schedule_id='...', schedule=[...], index=0, total_generated=1)