Investment Securities Available for Sale - Summary Of Available For Sale Investment Securities (Details) - USD ($) $ in Thousands	Dec. 31, 2022	Dec. 31, 2021
Debt Securities, Available-for-sale [Line Items]
Amortized Cost	$ 11,273,327	$ 10,991,506
Gross Unrealized Gains	2,560	66,427
Gross Unrealized Losses	(1,597,784)	(139,604)
Fair Value	9,678,103	10,918,329
U.S. Treasury securities
Debt Securities, Available-for-sale [Line Items]
Amortized Cost	515,953	120,465
Gross Unrealized Gains	0	0
Gross Unrealized Losses	(44,140)	(2,627)
Fair Value	471,813	117,838
U.S. Government agency securities
Debt Securities, Available-for-sale [Line Items]
Amortized Cost	52,411	53,214
Gross Unrealized Gains	0	1,374
Gross Unrealized Losses	(3,613)	(387)
Fair Value	48,798	54,201
Mortgage-backed securities issued by U.S. Government agencies
Debt Securities, Available-for-sale [Line Items]
Amortized Cost	904,593	790,329
Gross Unrealized Gains	1,624	768
Gross Unrealized Losses	(113,468)	(11,464)
Fair Value	792,749	779,633
Mortgage-backed securities issued by U.S. Government sponsored enterprises
Debt Securities, Available-for-sale [Line Items]
Amortized Cost	8,144,374	8,063,890
Gross Unrealized Gains	936	50,491
Gross Unrealized Losses	(1,250,240)	(102,080)
Fair Value	6,895,070	8,012,301
Collateralized mortgage obligations issued by U.S. Government agencies or sponsored enterprises
Debt Securities, Available-for-sale [Line Items]
Amortized Cost	769,498	951,691
Gross Unrealized Gains	0	4,658
Gross Unrealized Losses	(114,371)	(16,726)
Fair Value	655,127	939,623
Commercial mortgage-backed securities issued by U.S. Government agencies or sponsored enterprises
Debt Securities, Available-for-sale [Line Items]
Amortized Cost	877,590	479,420
Gross Unrealized Gains	0	8,644
Gross Unrealized Losses	(71,645)	(6,320)
Fair Value	805,945	481,744
Asset-backed securities
Debt Securities, Available-for-sale [Line Items]
Amortized Cost		514,188
Gross Unrealized Gains		0
Gross Unrealized Losses		0
Fair Value		514,188
Corporate debt securities and other debt securities
Debt Securities, Available-for-sale [Line Items]
Amortized Cost	8,908	18,309
Gross Unrealized Gains	0	492
Gross Unrealized Losses	(307)	0
Fair Value	$ 8,601	$ 18,801

Amount, before tax, of unrealized gain in accumulated other comprehensive income (AOCI) on investment in debt security measured at fair value with change in fair value recognized in other comprehensive income (available-for-sale).

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 320
-SubTopic 10
-Section 50
-Paragraph 2
-Subparagraph (b)
-URI https://asc.fasb.org/extlink&oid=126970911&loc=d3e27161-111563

+ Details

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

- Definition

Amount, before tax, of unrealized loss in accumulated other comprehensive income (AOCI) on investment in debt security measured at fair value with change in fair value recognized in other comprehensive income (available-for-sale).

+ References

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 320
-SubTopic 10
-Section 50
-Paragraph 2
-Subparagraph (c)
-URI https://asc.fasb.org/extlink&oid=126970911&loc=d3e27161-111563

+ Details

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

- Definition

Amortized cost of investment in debt security measured at fair value with change in fair value recognized in other comprehensive income (available-for-sale).

+ References

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 320
-SubTopic 10
-Section 50
-Paragraph 2
-Subparagraph (a)
-URI https://asc.fasb.org/extlink&oid=126970911&loc=d3e27161-111563

Reference 2: http://www.xbrl.org/2003/role/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 326
-SubTopic 30
-Section 45
-Paragraph 1
-URI https://asc.fasb.org/extlink&oid=124258926&loc=SL82898722-210454

+ Details

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

- Definition

Amount of investment in debt security measured at fair value with change in fair value recognized in other comprehensive income (available-for-sale).

+ References

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 942
-SubTopic 210
-Section S99
-Paragraph 1
-Subparagraph (SX 210.9-03(6))
-URI https://asc.fasb.org/extlink&oid=126897435&loc=d3e534808-122878

Reference 2: http://www.xbrl.org/2003/role/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 326
-SubTopic 30
-Section 45
-Paragraph 1
-URI https://asc.fasb.org/extlink&oid=124258926&loc=SL82898722-210454

Reference 3: http://www.xbrl.org/2003/role/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 320
-SubTopic 10
-Section 45
-Paragraph 1
-Subparagraph (b)
-URI https://asc.fasb.org/extlink&oid=124260329&loc=d3e26610-111562

Reference 4: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 320
-SubTopic 10
-Section 50
-Paragraph 2
-Subparagraph (aa)
-URI https://asc.fasb.org/extlink&oid=126970911&loc=d3e27161-111563

+ Details

Name:	us-gaap_AvailableForSaleSecuritiesDebtSecurities
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
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

No definition available.

+ Details

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

- Details

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

- Details

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

- Details

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

- Details

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

- Details

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

- Details

Name:	us-gaap_FinancialInstrumentAxis=syn_CommercialmortgagebackedsecuritiesissuedbyU.S.GovernmentsponsoredagenciesMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

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

- Details

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