Fair Value Measurements - Fair Value Measured on Recurring Basis (Details) - USD ($) $ in Thousands	Mar. 31, 2024	Sep. 30, 2023
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Available-for-sale securities, at fair value	$ 2,438,114	$ 1,995,097
Loans held for sale	2,993,658	0
Total financial assets	2,845,575	2,350,285
Recurring
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Available-for-sale securities, at fair value	2,438,114	1,995,097
Loans held for sale	2,993,658
Total financial assets	5,708,226	2,308,068
Total financial liabilities	64,020	79,668
Recurring | Client swap program hedges
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Derivative assets	63,264	78,797
Derivative liabilities	64,020	79,668
Recurring | Commercial loan fair value hedges
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Derivative assets	2,509	3,405
Recurring | Mortgage loan fair value hedges
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Derivative assets	56,093	46,396
Recurring | Borrowings cash flow hedges
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Derivative assets	154,588	184,373
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
Loans held for sale	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 2
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Available-for-sale securities, at fair value	2,438,114	1,995,097
Loans held for sale	2,993,658
Total financial assets	5,708,226	2,308,068
Total financial liabilities	64,020	79,668
Recurring | Level 2 | Client swap program hedges
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Derivative assets	63,264	78,797
Derivative liabilities	64,020	79,668
Recurring | Level 2 | Commercial loan fair value hedges
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Derivative assets	2,509	3,405
Recurring | Level 2 | Mortgage loan fair value hedges
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Derivative assets	56,093	46,396
Recurring | Level 2 | Borrowings cash flow hedges
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Derivative assets	154,588	184,373
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
Loans held for sale	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
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	312,199	217,053
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	312,199	217,053
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	549,463	588,016
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	549,463	588,016
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	35,061	34,662
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	35,061	34,662
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	249,743	242,522
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	249,743	242,522
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	1,291,648	912,844
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	1,291,648	912,844
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