Pension and Other Postretirement Benefit Plans - Schedule of Pension Plans Recognized in Accumulated Other Comprehensive Loss (Details) - USD ($) $ in Thousands	12 Months Ended
	Sep. 29, 2023	Sep. 30, 2022	Oct. 01, 2021
Reclassification adjustments:
Total	$ 18,297	$ (87,166)	$ (104,165)
Pension Plan | U.S. Plans
Arising during the period:
Net actuarial (gains) losses	(4,032)	578	(25,109)
Prior service cost	0	0	0
Total	(4,032)	578	(25,109)
Reclassification adjustments:
Net actuarial gains (losses)	1,335	(2,157)	(3,204)
Prior service benefit	(324)	(324)	(325)
Total	1,011	(2,481)	(3,529)
Total	(3,021)	(1,903)	(28,638)
Pension Plan | Non-U.S. Plans
Arising during the period:
Net actuarial (gains) losses	27,188	(78,705)	(65,547)
Prior service cost	0	0	0
Total	27,188	(78,705)	(65,547)
Reclassification adjustments:
Net actuarial gains (losses)	(4,802)	(5,492)	(8,761)
Prior service benefit	(1,068)	(1,066)	(1,219)
Total	(5,870)	(6,558)	(9,980)
Total	$ 21,318	$ (85,263)	$ (75,527)