Goodwill and Intangible Assets - Changes in Carrying Value of Goodwill (Details) - USD ($) $ in Thousands	12 Months Ended
	Oct. 01, 2023	Oct. 02, 2022
Goodwill [Roll Forward]
Balance at beginning of the period	$ 1,110,412	$ 1,108,578
Goodwill reallocation		0
Acquisitions	759,876	68,683
Translation and other	9,956	(66,849)
Balance at end of the period	1,880,244	1,110,412
GSG
Goodwill [Roll Forward]
Balance at beginning of the period	519,102	538,433
Goodwill reallocation		(51,497)
Acquisitions	138,380	42,365
Translation and other	2,460	(10,199)
Balance at end of the period	659,942	519,102
CIG
Goodwill [Roll Forward]
Balance at beginning of the period	591,310	570,145
Goodwill reallocation		51,497
Acquisitions	621,496	26,318
Translation and other	7,496	(56,650)
Balance at end of the period	$ 1,220,302	$ 591,310