Goodwill and Intangible Assets - Narrative (Details) $ in Thousands		1 Months Ended	3 Months Ended	12 Months Ended
	Jun. 30, 2025 USD ($)	Feb. 28, 2025 USD ($)	Mar. 30, 2025 USD ($)	Sep. 28, 2025 USD ($)	Sep. 29, 2024 USD ($)	Oct. 01, 2023 USD ($)	Jan. 20, 2025 contract
Goodwill [Line Items]
Impairment of goodwill	$ 0			$ 92,416	$ 0	$ 0
Percentage of excess of fair value over carrying value (less than)	38.00%
Percentage of cancellation programs							83.00%
Number of contracts cancelled | contract							5,200
Goodwill				2,049,874	2,046,569	1,880,244
Amortization of intangible assets				37,100	50,000	41,200
Reduction in intangible assets, foreign currency translation adjustment				0	13,400
Global Development Services
Goodwill [Line Items]
Impairment of goodwill		$ 92,400	$ 92,400
Goodwill		$ 130,500		38,100
GSG
Goodwill [Line Items]
Impairment of goodwill				92,416
Goodwill				658,511	750,817	659,942
Gross amounts of goodwill				768,600	768,500
Accumulated impairment				110,100	17,700
CIG
Goodwill [Line Items]
Impairment of goodwill				0
Goodwill				1,391,363	1,295,752	$ 1,220,302
Gross amounts of goodwill				1,512,900	1,417,300
Accumulated impairment				$ 121,500	$ 121,500