Fair Value Measurements - Fair Value by Balance Sheet Grouping (Details) - USD ($) $ in Thousands	Jun. 30, 2024	Sep. 30, 2023
Fair Value, Balance Sheet Grouping, Financial Statement Captions [Line Items]
Available-for-sale securities, at fair value	$ 2,428,769	$ 1,995,097
Held-to-maturity securities, at amortized cost	447,638	423,586
Loans held for sale	468,527	0
FHLB stock	107,282	126,820
Agency pass-through certificates
Fair Value, Balance Sheet Grouping, Financial Statement Captions [Line Items]
Held-to-maturity securities, at amortized cost	447,638	423,586
Carrying Amount
Fair Value, Balance Sheet Grouping, Financial Statement Captions [Line Items]
Available-for-sale securities, at fair value	2,428,769	1,995,097
Held-to-maturity securities, at amortized cost	447,638	423,586
Carrying Amount | Level 1
Fair Value, Balance Sheet Grouping, Financial Statement Captions [Line Items]
Cash and cash equivalents	2,492,504	980,649
Carrying Amount | Level 2
Fair Value, Balance Sheet Grouping, Financial Statement Captions [Line Items]
Loans held for sale	468,527	0
FHLB stock	107,282	126,820
Time deposits	9,255,760	5,305,016
Carrying Amount | Level 2 | Borrowings
Fair Value, Balance Sheet Grouping, Financial Statement Captions [Line Items]
Debt	3,934,514	3,650,000
Carrying Amount | Level 2 | Senior Debt
Fair Value, Balance Sheet Grouping, Financial Statement Captions [Line Items]
Debt	94,361	0
Carrying Amount | Level 2 | Client swap program hedges
Fair Value, Balance Sheet Grouping, Financial Statement Captions [Line Items]
Other assets	63,374	78,797
Other liabilities - client swap program hedges	64,075	79,668
Carrying Amount | Level 2 | Commercial loan fair value hedges
Fair Value, Balance Sheet Grouping, Financial Statement Captions [Line Items]
Other assets	2,534	3,405
Carrying Amount | Level 2 | Mortgage loan fair value hedges
Fair Value, Balance Sheet Grouping, Financial Statement Captions [Line Items]
Other assets	59,243	46,396
Carrying Amount | Level 2 | Borrowings cash flow hedges
Fair Value, Balance Sheet Grouping, Financial Statement Captions [Line Items]
Other assets	151,333	184,373
Carrying Amount | Level 2 | U.S. government and agency securities
Fair Value, Balance Sheet Grouping, Financial Statement Captions [Line Items]
Available-for-sale securities, at fair value	292,775	217,053
Carrying Amount | Level 2 | Asset-backed securities
Fair Value, Balance Sheet Grouping, Financial Statement Captions [Line Items]
Available-for-sale securities, at fair value	507,812	588,016
Carrying Amount | Level 2 | Municipal bonds
Fair Value, Balance Sheet Grouping, Financial Statement Captions [Line Items]
Available-for-sale securities, at fair value	35,017	34,662
Carrying Amount | Level 2 | Corporate debt securities
Fair Value, Balance Sheet Grouping, Financial Statement Captions [Line Items]
Available-for-sale securities, at fair value	241,167	242,522
Carrying Amount | Level 2 | Agency pass-through certificates
Fair Value, Balance Sheet Grouping, Financial Statement Captions [Line Items]
Available-for-sale securities, at fair value	1,351,998	912,844
Held-to-maturity securities, at amortized cost	447,638	423,586
Carrying Amount | Level 3
Fair Value, Balance Sheet Grouping, Financial Statement Captions [Line Items]
Loans receivable	20,873,919	17,476,550
Carrying Amount | Level 3 | Junior subordinated deferrable interest debentures
Fair Value, Balance Sheet Grouping, Financial Statement Captions [Line Items]
Debt	50,485	0
Estimated Fair Value
Fair Value, Balance Sheet Grouping, Financial Statement Captions [Line Items]
Available-for-sale securities, at fair value	2,428,769	1,995,097
Held-to-maturity securities, at amortized cost	398,005	355,188
Estimated Fair Value | Level 1
Fair Value, Balance Sheet Grouping, Financial Statement Captions [Line Items]
Cash and cash equivalents	2,492,504	980,649
Estimated Fair Value | Level 2
Fair Value, Balance Sheet Grouping, Financial Statement Captions [Line Items]
Loans held for sale	468,527	0
FHLB stock	107,282	126,820
Time deposits	9,188,683	5,232,689
Estimated Fair Value | Level 2 | Borrowings
Fair Value, Balance Sheet Grouping, Financial Statement Captions [Line Items]
Debt	3,929,935	3,653,229
Estimated Fair Value | Level 2 | Senior Debt
Fair Value, Balance Sheet Grouping, Financial Statement Captions [Line Items]
Debt	94,752	0
Estimated Fair Value | Level 2 | Client swap program hedges
Fair Value, Balance Sheet Grouping, Financial Statement Captions [Line Items]
Other assets	63,374	78,797
Other liabilities - client swap program hedges	64,075	79,668
Estimated Fair Value | Level 2 | Commercial loan fair value hedges
Fair Value, Balance Sheet Grouping, Financial Statement Captions [Line Items]
Other assets	2,534	3,405
Estimated Fair Value | Level 2 | Mortgage loan fair value hedges
Fair Value, Balance Sheet Grouping, Financial Statement Captions [Line Items]
Other assets	59,243	46,396
Estimated Fair Value | Level 2 | Borrowings cash flow hedges
Fair Value, Balance Sheet Grouping, Financial Statement Captions [Line Items]
Other assets	151,333	184,373
Estimated Fair Value | Level 2 | U.S. government and agency securities
Fair Value, Balance Sheet Grouping, Financial Statement Captions [Line Items]
Available-for-sale securities, at fair value	292,775	217,053
Estimated Fair Value | Level 2 | Asset-backed securities
Fair Value, Balance Sheet Grouping, Financial Statement Captions [Line Items]
Available-for-sale securities, at fair value	507,812	588,016
Estimated Fair Value | Level 2 | Municipal bonds
Fair Value, Balance Sheet Grouping, Financial Statement Captions [Line Items]
Available-for-sale securities, at fair value	35,017	34,662
Estimated Fair Value | Level 2 | Corporate debt securities
Fair Value, Balance Sheet Grouping, Financial Statement Captions [Line Items]
Available-for-sale securities, at fair value	241,167	242,522
Estimated Fair Value | Level 2 | Agency pass-through certificates
Fair Value, Balance Sheet Grouping, Financial Statement Captions [Line Items]
Available-for-sale securities, at fair value	1,351,998	912,844
Held-to-maturity securities, at amortized cost	398,005	355,188
Estimated Fair Value | Level 3
Fair Value, Balance Sheet Grouping, Financial Statement Captions [Line Items]
Loans receivable	20,038,322	16,559,758
Estimated Fair Value | Level 3 | Junior subordinated deferrable interest debentures
Fair Value, Balance Sheet Grouping, Financial Statement Captions [Line Items]
Debt	$ 50,535	$ 0