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Restructuring Activities - Schedule of Restructuring Liability (Details) - USD ($) $ in Millions	3 Months Ended
	Sep. 27, 2025	Sep. 28, 2024
Restructuring Reserve [Roll Forward]
Payments	$ (2.5)	$ (14.2)
Fiscal 2026 Restructuring Plan
Restructuring Reserve [Roll Forward]
Beginning balance	0.0
Charges	1.7
Payments	(1.3)
Ending balance	$ 0.4

X

- Definition

Restructuring Charges, Excluding Asset Write Off

+ References

No definition available.

+ Details

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Namespace Prefix:	syna_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	duration

X

- Definition

Amount of cash payments made as the result of exit or disposal activities. Excludes payments associated with a discontinued operation or an asset retirement obligation.

+ References

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Topic 420
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 1
-Subparagraph (b)(2)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147482017/420-10-50-1

Reference 2: http://www.xbrl.org/2009/role/commonPracticeRef
-Topic 230
-SubTopic 10
-Name Accounting Standards Codification
-Section 45
-Paragraph 17
-Subparagraph (f)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147482740/230-10-45-17

+ Details

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Namespace Prefix:	us-gaap_
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Balance Type:	credit
Period Type:	duration

X

- Definition

Carrying amount (including both current and noncurrent portions of the accrual) as of the balance sheet date pertaining to a specified type of cost associated with exit from or disposal of business activities or restructuring pursuant to a duly authorized plan.

+ References

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Topic 420
-SubTopic 10
-Name Accounting Standards Codification
-Section S99
-Paragraph 2
-Subparagraph (SAB Topic 5.P.4.b.2)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147479823/420-10-S99-2

Reference 2: http://www.xbrl.org/2003/role/disclosureRef
-Topic 420
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 1
-Subparagraph (b)(2)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147482017/420-10-50-1

+ Details

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Balance Type:	credit
Period Type:	instant

X

- Definition

A roll forward is a reconciliation of a concept from the beginning of a period to the end of a period.

+ References

No definition available.

+ Details

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Namespace Prefix:	us-gaap_
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Balance Type:	na
Period Type:	duration

X

- Details

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Period Type: