Derivative Instruments and Hedging Activities - Schedule of Effect of Hedging Derivative Instruments in the Consolidated Statements of Income (Details) - USD ($) $ in Thousands	3 Months Ended	9 Months Ended
Sep. 30, 2025	Sep. 30, 2024	Sep. 30, 2025	Sep. 30, 2024
Derivative [Line Items]
Loans, including fees	$ 680,441	$ 700,657	$ 1,986,504	$ 2,093,942
Deposits	281,523	345,314	842,157	1,013,734
Long-term debt	38,668	24,055	102,102	82,041
Loans, including fees \| Cash Flow Hedges
Derivative [Line Items]
Pre-tax income (loss) recognized on cash flow hedges	(13,993)	(36,768)	(49,119)	(113,118)
Loans, including fees \| Fair Value Hedges
Derivative [Line Items]
Pre-tax income (loss) recognized on cash flow hedges	0	0	0	0
Amounts related to interest settlements on derivatives	0	0	0	0
Recognized on derivatives	0	0	0	0
Recognized on hedged items	0	0	0	0
Loans, including fees \| Interest Rate Contract \| Cash Flow Hedges
Derivative [Line Items]
Realized gains (losses) reclassified from AOCI, pre-tax, to interest income on loans	(13,993)	(36,768)	(49,119)	(113,118)
Deposits \| Cash Flow Hedges
Derivative [Line Items]
Pre-tax income (loss) recognized on cash flow hedges	0	0	0	0
Deposits \| Fair Value Hedges
Derivative [Line Items]
Pre-tax income (loss) recognized on cash flow hedges	(1,559)	(5,626)	(6,810)	(18,151)
Amounts related to interest settlements on derivatives	(1,559)	(5,626)	(6,810)	(18,151)
Recognized on derivatives	1,056	15,078	12,645	15,480
Recognized on hedged items	(1,056)	(15,078)	(12,645)	(15,480)
Deposits \| Interest Rate Contract \| Cash Flow Hedges
Derivative [Line Items]
Realized gains (losses) reclassified from AOCI, pre-tax, to interest income on loans	0	0	0	0
Long-term debt \| Cash Flow Hedges
Derivative [Line Items]
Pre-tax income (loss) recognized on cash flow hedges	0	0	0	0
Long-term debt \| Fair Value Hedges
Derivative [Line Items]
Pre-tax income (loss) recognized on cash flow hedges	(1,280)	(3,052)	(5,591)	(10,394)
Amounts related to interest settlements on derivatives	(1,280)	(3,052)	(5,591)	(10,394)
Recognized on derivatives	(3,169)	14,490	19,158	13,486
Recognized on hedged items	3,169	(14,490)	(19,158)	(13,486)
Long-term debt \| Interest Rate Contract \| Cash Flow Hedges
Derivative [Line Items]
Realized gains (losses) reclassified from AOCI, pre-tax, to interest income on loans	$ 0	$ 0	$ 0	$ 0

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

No definition available.

Name:	syn_IncreaseDecreaseInFairValueOfAmountsRelatedToInterestSettlementsOnDerivatives
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

Reference 2: http://www.xbrl.org/2003/role/exampleRef
-Name Accounting Standards Codification
-Section 55
-Paragraph 10
-SubTopic 10
-Topic 825
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147482881/825-10-55-10

+ 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/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

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://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

Reference 2: http://www.xbrl.org/2009/role/commonPracticeRef
-Topic 815
-SubTopic 10
-Name Accounting Standards Codification
-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://www.xbrl.org/2003/role/exampleRef
-Topic 220
-SubTopic 40
-Name Accounting Standards Codification
-Section 55
-Paragraph 21
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147476153/220-40-55-21

Reference 2: 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: