Share-based Compensation and Other Employment Benefit Plans - Narrative (Details) $ in Millions	12 Months Ended
Dec. 31, 2022 USD ($) simulation shares	Dec. 31, 2021 USD ($) shares	Dec. 31, 2020 USD ($) shares
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Award requisite service period	3 years
Unrecognized compensation cost	$ 31.8
Unrecognized compensation cost, period of recognition (years)	1 year 10 months 2 days
Stock option grants (in shares) \| shares	0	0	0
Options outstanding, intrinsic value	$ 15.8
Options outstanding, weighted average remaining contractual term (years)	1 year 9 months 3 days
Options exercised, intrinsic value	$ 10.0	$ 21.3	$ 5.3
Stock purchase plans compensation expense	$ 1.1	1.1	1.1
Performance Share Units
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Number of simulations \| simulation	100,000
Non-option awards vested, total fair value	$ 2.2	$ 2.4	$ 7.9
Performance Share Units (PSUs)
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Vesting period	3 years
Percentage of awards subject to market condition	50.00%	50.00%	50.00%
Percentage of awards subject to ROATCE	50.00%
Restricted Share Units
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Non-option awards vested, total fair value	$ 28.0	$ 19.8	$ 13.4
Minimum \| Performance Share Units (PSUs)
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Options, vested and expected to vest, range based on return on average assets	0.00%
Maximum \| Performance Share Units (PSUs)
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Options, vested and expected to vest, range based on return on average assets	150.00%
2021 Omnibus Plan
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Shares of authorized but unissued common stock reserved for future grants (in shares) \| shares	5,800,000
Common stock, reserved for future issuance (in shares) \| shares	5,200,000

Share-based Compensation Arrangement by Share-based Payment Award, Percentage Of Awards Subject To Market Condition

No definition available.

Name:	syn_ShareBasedCompensationArrangementByShareBasedPaymentAwardPercentageOfAwardsSubjectToMarketCondition
Namespace Prefix:	syn_
Data Type:	dtr-types:percentItemType
Balance Type:	na
Period Type:	duration

- Definition

Share-based Compensation Arrangement by Share-based Payment Award, Percentage Of Awards Subject To ROATCE

+ References

No definition available.

+ Details

Name:	syn_ShareBasedCompensationArrangementByShareBasedPaymentAwardPercentageOfAwardsSubjectToROATCE
Namespace Prefix:	syn_
Data Type:	dtr-types:percentItemType
Balance Type:	na
Period Type:	duration

- Definition

Share-based Compensation Arrangement by Share-based Payment Award, Fair Value Assumptions, Number of Simulations

+ References

No definition available.

+ Details

Name:	syn_SharebasedCompensationArrangementbySharebasedPaymentAwardFairValueAssumptionsNumberofSimulations
Namespace Prefix:	syn_
Data Type:	xbrli:integerItemType
Balance Type:	na
Period Type:	duration

- Definition

Share-based Compensation Arrangement by Share-based Payment Award, Other than Options, Vested and Expected to Vest, Range Based on Return on Average Assets (ROAA)

+ References

No definition available.

+ Details

Name:	syn_SharebasedCompensationArrangementbySharebasedPaymentAwardOtherthanOptionsVestedandExpectedtoVestRangeBasedonReturnonAverageAssetsROAA
Namespace Prefix:	syn_
Data Type:	dtr-types:percentItemType
Balance Type:	na
Period Type:	instant

- Definition

Aggregate number of common shares reserved for future issuance.

+ References

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 210
-SubTopic 10
-Section S99
-Paragraph 1
-Subparagraph (SX 210.5-02.29)
-URI https://asc.fasb.org/extlink&oid=120391452&loc=d3e13212-122682

+ Details

Name:	us-gaap_CommonStockCapitalSharesReservedForFutureIssuance
Namespace Prefix:	us-gaap_
Data Type:	xbrli:sharesItemType
Balance Type:	na
Period Type:	instant

- Definition

The compensation expense recognized during the period pertaining to the deferred compensation arrangement.

+ References

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 718
-SubTopic 10
-Section 50
-Paragraph 1
-Subparagraph (b)
-URI https://asc.fasb.org/extlink&oid=128089324&loc=d3e5047-113901

Reference 2: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 710
-SubTopic 10
-Section 30
-Paragraph 1
-URI https://asc.fasb.org/extlink&oid=6409875&loc=d3e20015-108363

+ Details

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

- Definition

Amount of cost not yet recognized for nonvested award under share-based payment arrangement.

+ References

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 718
-SubTopic 10
-Section 50
-Paragraph 2
-Subparagraph (i)
-URI https://asc.fasb.org/extlink&oid=128089324&loc=d3e5070-113901

+ Details

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

- Definition

Weighted-average period over which cost not yet recognized is expected to be recognized for award under share-based payment arrangement, in 'PnYnMnDTnHnMnS' format, for example, 'P1Y5M13D' represents reported fact of one year, five months, and thirteen days.

+ References

+ Details

Name:	us-gaap_EmployeeServiceShareBasedCompensationNonvestedAwardsTotalCompensationCostNotYetRecognizedPeriodForRecognition1
Namespace Prefix:	us-gaap_
Data Type:	xbrli:durationItemType
Balance Type:	na
Period Type:	duration

- Definition

Estimated period over which an employee is required to provide service in exchange for the equity-based payment award, in 'PnYnMnDTnHnMnS' format, for example, 'P1Y5M13D' represents the reported fact of one year, five months, and thirteen days.

+ References

Reference 1: http://www.xbrl.org/2003/role/exampleRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 718
-SubTopic 10
-Section 50
-Paragraph 2
-Subparagraph (a)(1)
-URI https://asc.fasb.org/extlink&oid=128089324&loc=d3e5070-113901

+ Details

Name:	us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardAwardRequisiteServicePeriod1
Namespace Prefix:	us-gaap_
Data Type:	xbrli:durationItemType
Balance Type:	na
Period Type:	duration

- Definition

Period over which grantee's right to exercise award under share-based payment arrangement is no longer contingent on satisfaction of service or performance condition, in 'PnYnMnDTnHnMnS' format, for example, 'P1Y5M13D' represents reported fact of one year, five months, and thirteen days. Includes, but is not limited to, combination of market, performance or service condition.

+ References

+ Details

Name:	us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardAwardVestingPeriod1
Namespace Prefix:	us-gaap_
Data Type:	xbrli:durationItemType
Balance Type:	na
Period Type:	duration

- Definition

Fair value of share-based awards for which the grantee gained the right by satisfying service and performance requirements, to receive or retain shares or units, other instruments, or cash.

+ References

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 718
-SubTopic 10
-Section 50
-Paragraph 2
-Subparagraph (d)(2)
-URI https://asc.fasb.org/extlink&oid=128089324&loc=d3e5070-113901

+ Details

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

No definition available.

+ Details

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

- Definition

Number of shares authorized for issuance under share-based payment arrangement.

+ References

Reference 1: http://www.xbrl.org/2003/role/exampleRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 718
-SubTopic 10
-Section 50
-Paragraph 2
-Subparagraph (a)(3)
-URI https://asc.fasb.org/extlink&oid=128089324&loc=d3e5070-113901

+ Details

Name:	us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardNumberOfSharesAuthorized
Namespace Prefix:	us-gaap_
Data Type:	xbrli:sharesItemType
Balance Type:	na
Period Type:	instant

- Definition

Amount of accumulated difference between fair value of underlying shares on dates of exercise and exercise price on options exercised (or share units converted) into shares.

+ References

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 718
-SubTopic 10
-Section 50
-Paragraph 2
-Subparagraph (d)(2)
-URI https://asc.fasb.org/extlink&oid=128089324&loc=d3e5070-113901

+ Details

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

- Definition

Gross number of share options (or share units) granted during the period.

+ References

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 718
-SubTopic 10
-Section 50
-Paragraph 2
-Subparagraph (c)(1)(iv)(01)
-URI https://asc.fasb.org/extlink&oid=128089324&loc=d3e5070-113901

+ Details

Name:	us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsGrantsInPeriodGross
Namespace Prefix:	us-gaap_
Data Type:	xbrli:sharesItemType
Balance Type:	na
Period Type:	duration

- Definition

Amount by which the current fair value of the underlying stock exceeds the exercise price of options outstanding.

+ References

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 718
-SubTopic 10
-Section 50
-Paragraph 2
-URI https://asc.fasb.org/extlink&oid=128089324&loc=d3e5070-113901

+ Details

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

- Definition

Weighted average remaining contractual term for option awards outstanding, in 'PnYnMnDTnHnMnS' format, for example, 'P1Y5M13D' represents the reported fact of one year, five months, and thirteen days.

+ References

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 718
-SubTopic 10
-Section 50
-Paragraph 2
-Subparagraph (e)(1)
-URI https://asc.fasb.org/extlink&oid=128089324&loc=d3e5070-113901

+ Details

Name:	us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardOptionsOutstandingWeightedAverageRemainingContractualTerm2
Namespace Prefix:	us-gaap_
Data Type:	xbrli:durationItemType
Balance Type:	na
Period Type:	duration

- Details

Name:	us-gaap_AwardTypeAxis=syn_PerformanceRestrictedStockUnitsMRSUsMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_AwardTypeAxis=syn_PerformanceShareUnitsPSUsMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_AwardTypeAxis=us-gaap_RestrictedStockUnitsRSUMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	srt_RangeAxis=srt_MinimumMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	srt_RangeAxis=srt_MaximumMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_PlanNameAxis=syn_A2021OmnibusPlanMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type: