Fair Value Measurements - Fair Value Measured on Recurring Basis (Details) - USD ($) $ in Thousands	Sep. 30, 2022	Sep. 30, 2021
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Available-for-sale securities, at fair value	$ 2,051,037	$ 2,138,259
Derivative Asset, Statement of Financial Position [Extensible Enumeration]	Other assets	Other assets
Total Financial Assets	$ 2,457,897	$ 2,517,806
Derivative Liability, Statement of Financial Position [Extensible Enumeration]	Accrued expenses and other liabilities	Accrued expenses and other liabilities
Recurring
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Available-for-sale securities, at fair value	$ 2,051,037	$ 2,138,259
Total Financial Assets	2,337,524	2,191,684
Total Financial Liabilities	67,260	14,801
Recurring \| Client swap program hedges
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Derivative assets	67,260	10,983
Derivative liabilities	67,260	10,983
Recurring \| Commercial loan fair value hedges
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Derivative assets	2,517
Derivative liabilities		2,177
Recurring \| Mortgage loan fair value hedges
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Derivative assets	36,765
Derivative liabilities		1,641
Recurring \| Borrowing hedges
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Derivative assets	179,945	42,442
Recurring \| Level 1
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Available-for-sale securities, at fair value	0	0
Total Financial Assets	0	0
Total Financial Liabilities	0	0
Recurring \| Level 1 \| Client swap program hedges
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Derivative assets	0	0
Derivative liabilities	0	0
Recurring \| Level 1 \| Commercial loan fair value hedges
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Derivative assets	0
Derivative liabilities		0
Recurring \| Level 1 \| Mortgage loan fair value hedges
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Derivative assets	0
Derivative liabilities		0
Recurring \| Level 1 \| Borrowing hedges
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Derivative assets	0	0
Recurring \| Level 2
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Available-for-sale securities, at fair value	2,051,037	2,138,259
Total Financial Assets	2,337,524	2,191,684
Total Financial Liabilities	67,260	14,801
Recurring \| Level 2 \| Client swap program hedges
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Derivative assets	67,260	10,983
Derivative liabilities	67,260	10,983
Recurring \| Level 2 \| Commercial loan fair value hedges
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Derivative assets	2,517
Derivative liabilities		2,177
Recurring \| Level 2 \| Mortgage loan fair value hedges
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Derivative assets	36,765
Derivative liabilities		1,641
Recurring \| Level 2 \| Borrowing hedges
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Derivative assets	179,945	42,442
Recurring \| Level 3
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Available-for-sale securities, at fair value	0	0
Total Financial Assets	0	0
Total Financial Liabilities	0	0
Recurring \| Level 3 \| Client swap program hedges
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Derivative assets	0	0
Derivative liabilities	0	0
Recurring \| Level 3 \| Commercial loan fair value hedges
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Derivative assets	0
Derivative liabilities		0
Recurring \| Level 3 \| Mortgage loan fair value hedges
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Derivative assets	0
Derivative liabilities		0
Recurring \| Level 3 \| Borrowing hedges
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Derivative assets	0	0
U.S. government and agency securities \| Recurring
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Available-for-sale securities, at fair value	39,354	61,779
U.S. government and agency securities \| Recurring \| Level 1
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Available-for-sale securities, at fair value	0	0
U.S. government and agency securities \| Recurring \| Level 2
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Available-for-sale securities, at fair value	39,354	61,779
U.S. government and agency securities \| Recurring \| Level 3
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Available-for-sale securities, at fair value	0	0
Asset-backed securities \| Recurring
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Available-for-sale securities, at fair value	767,001	1,078,681
Asset-backed securities \| Recurring \| Level 1
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Available-for-sale securities, at fair value	0	0
Asset-backed securities \| Recurring \| Level 2
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Available-for-sale securities, at fair value	767,001	1,078,681
Asset-backed securities \| Recurring \| Level 3
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Available-for-sale securities, at fair value		0
Municipal bonds \| Recurring
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Available-for-sale securities, at fair value	34,962	39,984
Municipal bonds \| Recurring \| Level 1
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Available-for-sale securities, at fair value	0	0
Municipal bonds \| Recurring \| Level 2
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Available-for-sale securities, at fair value	34,962	39,984
Municipal bonds \| Recurring \| Level 3
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Available-for-sale securities, at fair value	0	0
Corporate debt securities \| Recurring
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Available-for-sale securities, at fair value	313,757	350,988
Corporate debt securities \| Recurring \| Level 1
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Available-for-sale securities, at fair value	0	0
Corporate debt securities \| Recurring \| Level 2
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Available-for-sale securities, at fair value	313,757	350,988
Corporate debt securities \| Recurring \| Level 3
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Available-for-sale securities, at fair value	0	0
Agency pass-through certificates \| Recurring
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Available-for-sale securities, at fair value	895,963	606,827
Agency pass-through certificates \| Recurring \| Level 1
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Available-for-sale securities, at fair value	0	0
Agency pass-through certificates \| Recurring \| Level 2
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Available-for-sale securities, at fair value	895,963	606,827
Agency pass-through certificates \| Recurring \| Level 3
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Available-for-sale securities, at fair value	$ 0	$ 0

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

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