Fair Value Measurements - Recurring (Details) - USD ($) $ in Thousands	Mar. 31, 2023	Sep. 30, 2022
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Available-for-sale securities, at fair value	$ 2,006,286	$ 2,051,037
Total financial assets	2,407,362	2,457,897
Recurring
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Available-for-sale securities, at fair value	2,006,286	2,051,037
Total financial assets	2,242,213	2,337,524
Total financial liabilities	54,910	67,260
Recurring | Client swap program hedges
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Derivative assets	54,935	67,260
Derivative liabilities	54,910	67,260
Recurring | Commercial loan fair value hedges
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Derivative assets	1,854	2,517
Recurring | Mortgage loan fair value hedges
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Derivative assets	27,971	36,765
Recurring | Borrowings cash flow hedges
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Derivative assets	151,167	179,945
Recurring | U.S. government and agency securities
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Available-for-sale securities, at fair value	94,772	39,354
Recurring | Asset-backed securities
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Available-for-sale securities, at fair value	654,070	767,001
Recurring | Municipal bonds
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Available-for-sale securities, at fair value	35,297	34,962
Recurring | Corporate debt securities
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Available-for-sale securities, at fair value	322,403	313,757
Recurring | Agency pass-through certificates
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Available-for-sale securities, at fair value	899,744	895,963
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 | Borrowings cash flow hedges
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Derivative assets	0	0
Recurring | Level 1 | U.S. government and agency securities
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Available-for-sale securities, at fair value	0	0
Recurring | Level 1 | Asset-backed securities
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Available-for-sale securities, at fair value	0	0
Recurring | Level 1 | Municipal bonds
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Available-for-sale securities, at fair value	0	0
Recurring | Level 1 | Corporate debt securities
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Available-for-sale securities, at fair value	0	0
Recurring | Level 1 | Agency pass-through certificates
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Available-for-sale securities, at fair value	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	2,006,286	2,051,037
Total financial assets	2,242,213	2,337,524
Total financial liabilities	54,910	67,260
Recurring | Level 2 | Client swap program hedges
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Derivative assets	54,935	67,260
Derivative liabilities	54,910	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	1,854	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	27,971	36,765
Recurring | Level 2 | Borrowings cash flow hedges
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Derivative assets	151,167	179,945
Recurring | Level 2 | U.S. government and agency securities
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Available-for-sale securities, at fair value	94,772	39,354
Recurring | Level 2 | Asset-backed securities
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Available-for-sale securities, at fair value	654,070	767,001
Recurring | Level 2 | Municipal bonds
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Available-for-sale securities, at fair value	35,297	34,962
Recurring | Level 2 | Corporate debt securities
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Available-for-sale securities, at fair value	322,403	313,757
Recurring | Level 2 | Agency pass-through certificates
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Available-for-sale securities, at fair value	899,744	895,963
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 | Borrowings cash flow hedges
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Derivative assets	0	0
Recurring | Level 3 | U.S. government and agency securities
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Available-for-sale securities, at fair value	0	0
Recurring | Level 3 | Asset-backed securities
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Available-for-sale securities, at fair value	0
Recurring | Level 3 | Municipal bonds
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Available-for-sale securities, at fair value	0	0
Recurring | Level 3 | Corporate debt securities
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Available-for-sale securities, at fair value	0	0
Recurring | Level 3 | Agency pass-through certificates
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Available-for-sale securities, at fair value	$ 0	$ 0