Derivative Instruments and Hedging Activities - Schedule of Estimated Fair Value of Derivative Instruments included in the Consolidated Balance Sheets (Details) - USD ($) $ in Thousands	Sep. 30, 2025	Dec. 31, 2024
Designated as Hedging Instrument
Derivative [Line Items]
Estimated fair value of derivative assets	$ 125	$ 168
Estimated fair value of derivative liabilities	0	14,472
Not Designated as Hedging Instruments
Derivative [Line Items]
Estimated fair value of derivative assets	85,697	83,727
Estimated fair value of derivative liabilities	120,958	201,917
Not Designated as Hedging Instruments \| Interest rate contracts
Derivative [Line Items]
Notional Amount	18,050,806	14,653,252
Estimated fair value of derivative assets	84,723	81,099
Estimated fair value of derivative liabilities	117,782	201,847
Not Designated as Hedging Instruments \| Mortgage Derivatives \| Mortgage derivatives - interest rate lock commitments
Derivative [Line Items]
Notional Amount	51,828	34,649
Estimated fair value of derivative assets	974	434
Estimated fair value of derivative liabilities	0	0
Not Designated as Hedging Instruments \| Mortgage Derivatives \| Mortgage derivatives - forward commitments to sell fixed-rate mortgage loans
Derivative [Line Items]
Notional Amount	80,000	51,500
Estimated fair value of derivative assets	0	233
Estimated fair value of derivative liabilities	119	0
Not Designated as Hedging Instruments \| Risk participation agreements
Derivative [Line Items]
Notional Amount	1,057,038	924,267
Estimated fair value of derivative assets	0	0
Estimated fair value of derivative liabilities	21	6
Not Designated as Hedging Instruments \| Foreign exchange contracts
Derivative [Line Items]
Notional Amount	134,023	148,805
Estimated fair value of derivative assets	0	1,961
Estimated fair value of derivative liabilities	72	0
Not Designated as Hedging Instruments \| Visa derivative
Derivative [Line Items]
Notional Amount	0	0
Estimated fair value of derivative assets	0	0
Estimated fair value of derivative liabilities	2,964	64
Cash Flow Hedges
Derivative [Line Items]
Estimated fair value of derivative assets	65	0
Estimated fair value of derivative liabilities	0	13,003
Cash Flow Hedges \| Interest rate contracts
Derivative [Line Items]
Notional Amount	3,850,000	4,350,000
Estimated fair value of derivative assets	65	0
Estimated fair value of derivative liabilities	0	13,003
Fair Value Hedges
Derivative [Line Items]
Estimated fair value of derivative assets	60	168
Estimated fair value of derivative liabilities	0	1,469
Fair Value Hedges \| Interest rate contracts
Derivative [Line Items]
Notional Amount	1,652,967	2,102,967
Estimated fair value of derivative assets	60	168
Estimated fair value of derivative liabilities	$ 0	$ 1,469

Fair value, after offset of derivative liability, of financial asset or other contract with one or more underlyings, notional amount or payment provision or both, and the contract can be net settled by means outside the contract or delivery of an asset, before offset against an obligation to return collateral under a master netting arrangement. Includes assets elected not to be offset. Excludes assets not subject to a master netting arrangement.

Reference 1: http://www.xbrl.org/2009/role/commonPracticeRef
-Topic 815
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 7A
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147480434/815-10-50-7A

Reference 2: http://www.xbrl.org/2009/role/commonPracticeRef
-Topic 815
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 8
-Subparagraph (c)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147480434/815-10-50-8

Reference 3: http://www.xbrl.org/2009/role/commonPracticeRef
-Topic 210
-SubTopic 20
-Name Accounting Standards Codification
-Section 50
-Paragraph 3
-Subparagraph (c)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147483466/210-20-50-3

+ Details

Name:	us-gaap_DerivativeFairValueOfDerivativeAssetAmountNotOffsetAgainstCollateral
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	instant

- Definition

Fair value, after offset of derivative asset, of financial liability or contract with one or more underlyings, notional amount or payment provision or both, and the contract can be net settled by means outside the contract or delivery of an asset, elected not to be and before offset against a right to receive collateral under a master netting arrangement. Includes liabilities elected not to be offset. Excludes liabilities not subject to a master netting arrangement.

+ References

+ Details

Name:	us-gaap_DerivativeFairValueOfDerivativeLiabilityAmountNotOffsetAgainstCollateral
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	instant

- Definition

Line items represent financial concepts included in a table. These concepts are used to disclose reportable information associated with domain members defined in one or many axes to the table.

+ References

Reference 1: http://www.xbrl.org/2009/role/commonPracticeRef
-Topic 815
-SubTopic 20
-Name Accounting Standards Codification
-Section 25
-Paragraph 6A
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147480682/815-20-25-6A

Reference 2: http://www.xbrl.org/2003/role/disclosureRef
-Topic 815
-SubTopic 40
-Name Accounting Standards Codification
-Section 50
-Paragraph 5
-Subparagraph (f)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147480237/815-40-50-5

+ Details

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

- Definition

Nominal or face amount used to calculate payment on derivative.

+ References

Reference 1: http://www.xbrl.org/2003/role/exampleRef
-Topic 815
-SubTopic 10
-Name Accounting Standards Codification
-Section 55
-Paragraph 181
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147480401/815-10-55-181

Reference 2: http://www.xbrl.org/2009/role/commonPracticeRef
-Topic 815
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 1B
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147480434/815-10-50-1B

Reference 3: http://www.xbrl.org/2009/role/commonPracticeRef
-Topic 815
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 1A
-Subparagraph (d)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147480434/815-10-50-1A

+ Details

Name:	us-gaap_DerivativeNotionalAmount
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	na
Period Type:	instant

- Details

Name:	us-gaap_HedgingDesignationAxis=us-gaap_DesignatedAsHedgingInstrumentMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_HedgingDesignationAxis=us-gaap_NondesignatedMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_DerivativeInstrumentRiskAxis=us-gaap_InterestRateContractMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_DerivativeInstrumentRiskAxis=syn_MortgageDerivativeMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_FinancialInstrumentAxis=us-gaap_InterestRateLockCommitmentsMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_FinancialInstrumentAxis=syn_ForwardCommitmentsToSellFixedRateMortgageLoansMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_DerivativeInstrumentRiskAxis=syn_RiskParticipationAgreementsMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_DerivativeInstrumentRiskAxis=us-gaap_ForeignExchangeContractMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_DerivativeInstrumentRiskAxis=syn_VisaDerivativeMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_DerivativeInstrumentsGainLossByHedgingRelationshipAxis=us-gaap_CashFlowHedgingMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_DerivativeInstrumentsGainLossByHedgingRelationshipAxis=us-gaap_FairValueHedgingMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type: