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Fair Value Measurements - Schedule of financial assets measured at fair value on a recurring basis (Parenthetical) (Detail) - USD ($) $ in Millions	Sep. 30, 2023	Jun. 24, 2023
Fair Value Disclosures [Abstract]
Cash held in bank	$ 323.6	$ 853.9

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- Definition

Cash held in bank

+ References

No definition available.

+ Details

Name:	syna_CashHeldInBank
Namespace Prefix:	syna_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	instant

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- References

No definition available.

+ Details

Name:	us-gaap_FairValueDisclosuresAbstract
Namespace Prefix:	us-gaap_
Data Type:	xbrli:stringItemType
Balance Type:	na
Period Type:	duration