Goodwill and Intangible Assets - Changes in Carrying Value of Goodwill (Details) - USD ($) $ in Thousands		12 Months Ended
	Jun. 30, 2025	Sep. 28, 2025	Sep. 29, 2024	Oct. 01, 2023
Goodwill [Roll Forward]
Balance at beginning of the period		$ 2,046,569	$ 1,880,244
Acquisition activity		124,292	84,865
Impairment of goodwill	$ 0	(92,416)	0	$ 0
Classified as held-for-sale		(18,533)
Translation and other adjustments		(10,038)	81,460
Balance at end of the period		2,049,874	2,046,569	1,880,244
GSG
Goodwill [Roll Forward]
Balance at beginning of the period		750,817	659,942
Acquisition activity		0	84,865
Impairment of goodwill		(92,416)
Classified as held-for-sale		0
Translation and other adjustments		110	6,010
Balance at end of the period		658,511	750,817	659,942
CIG
Goodwill [Roll Forward]
Balance at beginning of the period		1,295,752	1,220,302
Acquisition activity		124,292	0
Impairment of goodwill		0
Classified as held-for-sale		(18,533)
Translation and other adjustments		(10,148)	75,450
Balance at end of the period		$ 1,391,363	$ 1,295,752	$ 1,220,302