Fair Value Measurements - Fair Value Measured on Recurring Basis (Details) - USD ($) $ in Thousands	Sep. 30, 2023	Sep. 30, 2022
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Available-for-sale securities, at fair value	$ 1,995,097	$ 2,051,037
Derivative Asset, Statement of Financial Position [Extensible Enumeration]	Other assets	Other assets
Total Financial Assets	$ 2,350,285	$ 2,457,897
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	$ 1,995,097	$ 2,051,037
Total Financial Assets	2,308,068	2,337,524
Total Financial Liabilities	79,668	67,260
Recurring | Client swap program hedges
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Derivative assets	78,797	67,260
Derivative liabilities	79,668	67,260
Recurring | Commercial loan fair value hedges
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Derivative assets	3,405	2,517
Recurring | Mortgage loan fair value hedges
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Derivative assets	46,396	36,765
Recurring | Borrowing hedges
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Derivative assets	184,373	179,945
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	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	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	1,995,097	2,051,037
Total Financial Assets	2,308,068	2,337,524
Total Financial Liabilities	79,668	67,260
Recurring | Level 2 | Client swap program hedges
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Derivative assets	78,797	67,260
Derivative liabilities	79,668	67,260
Recurring | Level 2 | Commercial loan fair value hedges
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Derivative assets	3,405	2,517
Recurring | Level 2 | Mortgage loan fair value hedges
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Derivative assets	46,396	36,765
Recurring | Level 2 | Borrowing hedges
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Derivative assets	184,373	179,945
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	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	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	217,053	39,354
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	217,053	39,354
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 due | Recurring
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Available-for-sale securities, at fair value	588,016	767,001
Asset-backed securities due | 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 due | Recurring | Level 2
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Available-for-sale securities, at fair value	588,016	767,001
Asset-backed securities due | 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	34,662	34,962
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	34,662	34,962
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	242,522	313,757
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	242,522	313,757
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	912,844	895,963
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	912,844	895,963
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