Stock-Based Compensation and Warrant Units - Schedule of Performance Share Unit Activity (Details) - PSU - $ / shares	12 Months Ended
	Sep. 28, 2024	Sep. 30, 2023
Shares
Balance at beginning of period (in shares)	337,986	0
Granted (in shares)	235,292	337,986
Vested (in shares)	0	0
Forfeited (in shares)	(73,226)	0
Balance at end of period (in shares)	500,052	337,986
Weighted Average Grant Date Fair Value
Balance at beginning of period (in dollars per share)	$ 15.56
Granted (in dollars per share)	48.38	15.56
Vested (in dollars per share)
Forfeited (in dollars per share)	15.56
Balance at end of period (in dollars per share)	$ 31.10	$ 15.56