Acquisitions and Divestitures - Narrative (Details) £ / shares in Units, $ / shares in Units, $ in Thousands, £ in Millions			3 Months Ended	12 Months Ended
	Jan. 23, 2023 USD ($)	Jan. 23, 2023 GBP (£)	Mar. 31, 2024 USD ($)	Sep. 28, 2025 USD ($)	Sep. 29, 2024 USD ($)	Oct. 01, 2023 USD ($) employee program $ / shares	Sep. 23, 2022 £ / shares
Business Combination [Line Items]
Goodwill				$ 2,049,874	$ 2,046,569	$ 1,880,244
Acquisition and integration expenses				0	7,138	33,169
Gain (loss) in contingent earn-out liabilities				12,200	(2,500)	(12,300)
LS Technologies
Business Combination [Line Items]
Fair value of acquisition purchase price			$ 120,000	147,000	$ 120,000
Initial cash payments			93,000	104,000
Cash holdback related to tax reserve			4,000	43,000
Equity interests issued and issuable			23,000
Net tangible assets			12,000	13,000
Intangible assets			23,000	14,000
Business combination, recognized liability assumed, deferred tax liability				4,000
Goodwill			85,000	$ 124,000
RPS Group PLC
Business Combination [Line Items]
Fair value of acquisition purchase price	$ 784,000	£ 633
Intangible assets	174,094
Business combination, recognized liability assumed, deferred tax liability	41,613
Goodwill	652,762
Acquisition and integration expenses						33,200
Net purchase price	675,000
Revenue						600,000
Net income (loss)						$ 3,600
Diluted earnings per share (in dollars per share) | $ / shares						$ 0.01
Intangible amortization						$ 26,800
Price of acquisition, expected, per share (in pounds per share) | £ / shares							£ 2.22
Amyx, Inc.
Business Combination [Line Items]
Fair value of acquisition purchase price						$ 120,900
Number of employees (over for Amyx) | employee						500
Number of government programs acquired (over) | program						30
Promissory note						$ 100,000
Payables (receivables) related to estimated post-closing adjustments						8,700
Contingent earn-out liability						12,200
Maximum potential payout at end of period						$ 25,000
Foreign Exchange Contract | RPS Group PLC
Business Combination [Line Items]
Foreign currency forward contract, asset fair value	$ 109,300
Minimum
Business Combination [Line Items]
Useful life of intangible assets				1 year
Significant unobservable input, earn-out period				3 years
Maximum
Business Combination [Line Items]
Useful life of intangible assets				12 years
Significant unobservable input, earn-out period				5 years
Maximum | LS Technologies
Business Combination [Line Items]
Equity interests issued and issuable			$ 60,000	$ 60,000