Goodwill and Intangible Assets - Changes in Carrying Value of Goodwill (Details) - USD ($) $ in Thousands	12 Months Ended
	Sep. 29, 2024	Oct. 01, 2023
Goodwill [Roll Forward]
Balance at beginning of the period	$ 1,880,244	$ 1,110,412
Acquisition activity	84,865	759,876
Translation and other adjustments	81,460	9,956
Balance at end of the period	2,046,569	1,880,244
GSG
Goodwill [Roll Forward]
Balance at beginning of the period	659,942	519,102
Acquisition activity	84,865	138,380
Translation and other adjustments	6,010	2,460
Balance at end of the period	750,817	659,942
CIG
Goodwill [Roll Forward]
Balance at beginning of the period	1,220,302	591,310
Acquisition activity	0	621,496
Translation and other adjustments	75,450	7,496
Balance at end of the period	$ 1,295,752	$ 1,220,302