Endpoint to execute a task asynchronously in the background.
Args: task_id (str): The unique identifier of the task to execute.
Returns: TaskOutcome: The result of the task execution, including metadata like status, output, timestamps, etc.
Raises: HTTPException 403: If the task is private and the current user is not its creator. HTTPException 404: If the task is not found. HTTPException 500: If an error occurs during execution.
JWT Authorization header using the Bearer scheme. Example: 'Authorization: Bearer {token}'
Successful Response
The task ID
The name of the task
The time the task execution started
The time the task execution completed
The result of the task execution
'completed' if all actions succeeded, else 'failed'