Derivatives and Hedging Activities - Schedule of Gains/(Losses) on Derivative Instruments in Fair Value and Cash Flow Accounting Hedging Relationships (Details) - USD ($) $ in Thousands	3 Months Ended	6 Months Ended
Mar. 31, 2026	Mar. 31, 2025	Mar. 31, 2026	Mar. 31, 2025
Derivative Instruments, Gain (Loss) [Line Items]
Interest income/(expense), including the effects of fair value and cash flow hedges	$ 262,148	$ 282,077	$ 526,355	$ 568,674
Interest on Mortgage-backed securities	44,341	23,926	83,243	42,263
Interest income/(expense), including the effects of fair value and cash flow hedges	(21,165)	(23,226)	(36,336)	(50,762)
Interest rate contracts \| Fair value hedging \| Interest income on loans receivable
Gain/(loss) on fair value hedging relationships:
Amounts related to interest settlements on derivatives	1,856	4,988	4,610	12,981
Recognized on derivatives	6,336	(20,773)	6,864	16,820
Recognized on hedged items	(6,447)	19,616	(6,992)	(23,802)
Net income/(expense) recognized on fair value hedges	1,745	3,831	4,482	5,999
Interest rate contracts \| Fair value hedging \| Interest on Mortgage-backed securities
Gain/(loss) on fair value hedging relationships:
Amounts related to interest settlements on derivatives	(428)	116	(332)	116
Recognized on derivatives	4,850	(8,682)	6,912	(8,682)
Recognized on hedged items	(4,895)	8,901	(6,989)	8,901
Net income/(expense) recognized on fair value hedges	(473)	335	(409)	335
Interest rate contracts \| Cash flow hedging \| Interest expense on FHLB advances
Gain/(loss) on cash flow hedging relationships:
Amounts related to interest settlements on derivatives	7,276	8,573	15,605	18,053
Amount of derivative gain/(loss) reclassified from AOCI into interest income/expense	0	0	0	0
Net income/(expense) recognized on cash flow hedges	$ 7,276	$ 8,573	$ 15,605	$ 18,053

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The aggregate interest and fee income generated by: (1) loans the Entity has positive intent and ability to hold for the foreseeable future, or until maturity or payoff, including commercial and consumer loans, whether domestic or foreign, which may consist of: (a) industrial and agricultural; (b) real estate; and (c) real estate construction loans; (d) trade financing; (e) lease financing; (f) home equity lines-of-credit; (g) automobile and other vehicle loans; and (h) credit card and other revolving-type loans and (2) loans and leases held-for-sale which may include mortgage loans, direct financing, and sales-type leases.

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