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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
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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