Derivative Instruments - Schedule of Effect of Hedging Derivative Instruments on the Consolidated Statements of Income (Details) - USD ($) $ in Thousands	12 Months Ended
Dec. 31, 2024	Dec. 31, 2023	Dec. 31, 2022
Derivative [Line Items]
Loans, including fees	$ 2,769,778	$ 2,684,762	$ 1,806,060
Deposits	1,329,932	1,026,755	187,232
Long-term debt	109,657	180,670	79,402
Interest Income, Loans, Including Fees \| Cash Flow Hedging
Derivative [Line Items]
Pre-tax income (loss) recognized on hedges	(139,041)	(176,442)	(24,057)
Interest Income, Loans, Including Fees \| Fair Value Hedging
Derivative [Line Items]
Pre-tax income (loss) recognized on hedges	0	0	0
Amounts related to interest settlements on derivatives	0	0	0
Recognized on derivatives	0	0	0
Recognized on hedged items	0	0	0
Interest Income, Loans, Including Fees \| Interest Rate Contracts \| Cash Flow Hedging
Derivative [Line Items]
Realized gains (losses) reclassified from AOCI, pre-tax, to interest income on loans	(139,041)	(176,442)	(24,057)
Deposits \| Cash Flow Hedging
Derivative [Line Items]
Pre-tax income (loss) recognized on hedges	0	0	0
Deposits \| Fair Value Hedging
Derivative [Line Items]
Pre-tax income (loss) recognized on hedges	(21,777)	(22,495)	1,516
Amounts related to interest settlements on derivatives	(21,777)	(22,495)	1,516
Recognized on derivatives	11,224	8,711	(24,227)
Recognized on hedged items	(11,224)		24,227
Deposits \| Interest Rate Contracts \| Cash Flow Hedging
Derivative [Line Items]
Realized gains (losses) reclassified from AOCI, pre-tax, to interest income on loans	0	0	0
Deposits \| Interest Rate Contracts \| Fair Value Hedging
Derivative [Line Items]
Recognized on hedged items		(8,711)
Long-term debt \| Cash Flow Hedging
Derivative [Line Items]
Pre-tax income (loss) recognized on hedges	0	0	0
Long-term debt \| Fair Value Hedging
Derivative [Line Items]
Pre-tax income (loss) recognized on hedges	(12,803)	(16,358)	(322)
Amounts related to interest settlements on derivatives	(12,803)	(16,358)	(322)
Recognized on derivatives	1,777	5,986	(19,348)
Recognized on hedged items	(1,777)		19,348
Long-term debt \| Interest Rate Contracts \| Cash Flow Hedging
Derivative [Line Items]
Realized gains (losses) reclassified from AOCI, pre-tax, to interest income on loans	$ 0	0	$ 0
Long-term debt \| Interest Rate Contracts \| Fair Value Hedging
Derivative [Line Items]
Recognized on hedged items		$ (5,986)

Increase (Decrease) In Fair Value Of Amounts Related To Interest Settlements And Amortization On Derivatives

No definition available.

Name:	syn_IncreaseDecreaseInFairValueOfAmountsRelatedToInterestSettlementsAndAmortizationOnDerivatives
Namespace Prefix:	syn_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	duration

- Definition

Realized Gains (Losses) Reclassified From AOCI, Pre-Tax, To Interest Income On Loans

+ References

No definition available.

+ Details

Name:	syn_RealizedGainsLossesReclassifiedFromAOCIPreTaxToInterestIncomeOnLoans
Namespace Prefix:	syn_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	duration

- Definition

Amount of increase (decrease) in the fair value of derivatives recognized in the income statement.

+ References

Reference 1: http://www.xbrl.org/2009/role/commonPracticeRef
-Topic 815
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 4A
-Subparagraph (b)(1)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147480434/815-10-50-4A

+ Details

Name:	us-gaap_DerivativeGainLossOnDerivativeNet
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	duration

- 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/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

Aggregate net gain (loss) on all derivative instruments recognized in earnings during the period, before tax effects.

+ References

+ Details

Name:	us-gaap_GainLossOnDerivativeInstrumentsNetPretax
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	duration

- Definition

Amount of unrealized gain (loss) included in earnings related to the fair value of the hedged item in an interest rate fair value hedge, offset by the gain (loss) on the hedging instrument to the extent that the fair value hedge is determined to be effective.

+ References

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Name Accounting Standards Codification
-Topic 815
-SubTopic 10
-Section 50
-Paragraph 4A
-Subparagraph (b)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147480434/815-10-50-4A

Reference 2: http://fasb.org/us-gaap/role/ref/legacyRef
-Name Accounting Standards Codification
-Topic 815
-SubTopic 10
-Section 50
-Paragraph 4C
-Subparagraph (a)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147480434/815-10-50-4C

+ Details

Name:	us-gaap_IncreaseDecreaseInFairValueOfHedgedItemInInterestRateFairValueHedge1
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	duration

- Definition

Interest and fee income generated by loans the Entity intends and has the ability to hold for the foreseeable future, or until maturity or payoff, including commercial and consumer loans, whether domestic or foreign, which may consist of: (1) industrial and agricultural; (2) real estate; and (3) real estate construction loans; (4) trade financing; (5) lease financing; (6) home equity lines-of-credit; (7) automobile and other vehicle loans; and (8) credit card and other revolving-type loans. Also includes interest income for leases held by the Entity.

+ References

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Topic 942
-SubTopic 220
-Name Accounting Standards Codification
-Section S99
-Paragraph 1
-Subparagraph (SX 210.9-04(1))
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147478524/942-220-S99-1

+ Details

Name:	us-gaap_InterestAndFeeIncomeLoansAndLeasesHeldInPortfolio
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	duration

- Definition

Aggregate amount of interest expense on all deposits.

+ References

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Topic 942
-SubTopic 220
-Name Accounting Standards Codification
-Section S99
-Paragraph 1
-Subparagraph (SX 210.9-04(6))
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147478524/942-220-S99-1

+ Details

Name:	us-gaap_InterestExpenseDeposits
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	duration

- Definition

Aggregate amount of interest paid or due on all long-term debt.

+ References

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Name Regulation S-K (SK)
-Number 229
-Section 1402
-Paragraph a
-Publisher SEC

Reference 2: http://www.xbrl.org/2003/role/disclosureRef
-Name Regulation S-K (SK)
-Number 229
-Section 1402
-Paragraph b
-Subparagraph (1)
-Publisher SEC

Reference 3: http://fasb.org/us-gaap/role/ref/legacyRef
-Topic 942
-SubTopic 220
-Name Accounting Standards Codification
-Section S99
-Paragraph 1
-Subparagraph (SX 210.9-04(8))
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147478524/942-220-S99-1

+ Details

Name:	us-gaap_InterestExpenseLongTermDebt
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	duration

- Details

Name:	us-gaap_FinancialInstrumentAxis=syn_InterestIncomeLoansIncludingFeesMember
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:

- Details

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

- Details

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

- Details

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