Stock-Based Compensation and Warrant Units - Schedule of Warrant Activity (Details) - Warrants - shares	12 Months Ended
	Sep. 28, 2024	Sep. 30, 2023
Class of Warrant or Right [Roll Forward]
Outstanding and unvested at beginning of period (in shares)	11,434,360	258,972
Granted (in shares)	0	11,434,360
Vested (in shares)	0	(258,972)
Outstanding and unvested at end of period (in shares)	11,434,360	11,434,360