Goodwill and Intangible Assets - Changes in Carrying Value of Goodwill (Details) - USD ($)		3 Months Ended	12 Months Ended
	Jun. 28, 2021	Sep. 27, 2020	Oct. 03, 2021	Sep. 27, 2020	Sep. 29, 2019
Goodwill [Roll Forward]
Balance at beginning of the period			$ 993,498,000	$ 924,820,000
Acquisitions			90,591,000	80,176,000
Impairment	$ 0	$ (15,800,000)	0	(15,800,000)	$ (7,755,000)
Translation and other			24,489,000	4,302,000
Balance at end of the period		993,498,000	1,108,578,000	993,498,000	924,820,000
GSG
Goodwill [Roll Forward]
Balance at beginning of the period			516,315,000	441,802,000
Acquisitions			15,112,000	74,882,000
Impairment				0
Translation and other			7,006,000	(369,000)
Balance at end of the period		516,315,000	538,433,000	516,315,000	441,802,000
CIG
Goodwill [Roll Forward]
Balance at beginning of the period			477,183,000	483,018,000
Acquisitions			75,479,000	5,294,000
Impairment				(15,800,000)
Translation and other			17,483,000	4,671,000
Balance at end of the period		$ 477,183,000	$ 570,145,000	$ 477,183,000	$ 483,018,000