Allowance for Losses on Loans - Credit Risk Profile Based on Payment Activity (Details) - USD ($) $ in Thousands	Jun. 30, 2024	Sep. 30, 2023
Financing Receivable, Credit Quality Indicator [Line Items]
Amount	$ 21,077,743	$ 17,653,757
Commercial loans
Financing Receivable, Credit Quality Indicator [Line Items]
Amount	12,246,080	10,507,610
Commercial loans | Multi-family
Financing Receivable, Credit Quality Indicator [Line Items]
Amount	4,513,323	2,886,594
Commercial loans | Commercial real estate
Financing Receivable, Credit Quality Indicator [Line Items]
Amount	3,746,945	3,310,101
Commercial loans | Commercial & industrial
Financing Receivable, Credit Quality Indicator [Line Items]
Amount	2,389,236	2,315,318
Commercial loans | Construction
Financing Receivable, Credit Quality Indicator [Line Items]
Amount	1,440,152	1,838,936
Commercial loans | Land - acquisition & development
Financing Receivable, Credit Quality Indicator [Line Items]
Amount	156,424	156,661
Consumer loans
Financing Receivable, Credit Quality Indicator [Line Items]
Amount	8,831,663	7,146,147
Consumer loans | Construction
Financing Receivable, Credit Quality Indicator [Line Items]
Amount	190,433	324,451
Consumer loans | Single-family residential
Financing Receivable, Credit Quality Indicator [Line Items]
Amount	8,186,361	6,388,990
Consumer loans | Land - consumer lot loans
Financing Receivable, Credit Quality Indicator [Line Items]
Amount	111,574	124,842
Consumer loans | HELOC
Financing Receivable, Credit Quality Indicator [Line Items]
Amount	258,833	237,754
Consumer loans | Consumer
Financing Receivable, Credit Quality Indicator [Line Items]
Amount	84,462	70,110
Performing Loans
Financing Receivable, Credit Quality Indicator [Line Items]
Amount	$ 21,016,475	$ 17,603,335
% of Total Loans	99.70%	99.70%
Performing Loans | Commercial loans
Financing Receivable, Credit Quality Indicator [Line Items]
Amount	$ 12,206,356	$ 10,472,966
% of Total Loans	99.70%	99.70%
Performing Loans | Commercial loans | Multi-family
Financing Receivable, Credit Quality Indicator [Line Items]
Amount	$ 4,503,339	$ 2,881,467
% of Total Loans	99.80%	99.80%
Performing Loans | Commercial loans | Commercial real estate
Financing Receivable, Credit Quality Indicator [Line Items]
Amount	$ 3,720,537	$ 3,286,666
% of Total Loans	99.30%	99.30%
Performing Loans | Commercial loans | Commercial & industrial
Financing Receivable, Credit Quality Indicator [Line Items]
Amount	$ 2,387,098	$ 2,309,236
% of Total Loans	99.90%	99.70%
Performing Loans | Commercial loans | Construction
Financing Receivable, Credit Quality Indicator [Line Items]
Amount	$ 1,439,032	$ 1,838,936
% of Total Loans	99.90%	100.00%
Performing Loans | Commercial loans | Land - acquisition & development
Financing Receivable, Credit Quality Indicator [Line Items]
Amount	$ 156,350	$ 156,661
% of Total Loans	100.00%	100.00%
Performing Loans | Consumer loans
Financing Receivable, Credit Quality Indicator [Line Items]
Amount	$ 8,810,119	$ 7,130,369
% of Total Loans	99.80%	99.80%
Performing Loans | Consumer loans | Construction
Financing Receivable, Credit Quality Indicator [Line Items]
Amount	$ 190,345	$ 324,363
% of Total Loans	100.00%	100.00%
Performing Loans | Consumer loans | Single-family residential
Financing Receivable, Credit Quality Indicator [Line Items]
Amount	$ 8,165,939	$ 6,374,072
% of Total Loans	99.80%	99.80%
Performing Loans | Consumer loans | Land - consumer lot loans
Financing Receivable, Credit Quality Indicator [Line Items]
Amount	$ 111,338	$ 124,833
% of Total Loans	99.80%	100.00%
Performing Loans | Consumer loans | HELOC
Financing Receivable, Credit Quality Indicator [Line Items]
Amount	$ 258,075	$ 237,018
% of Total Loans	99.70%	99.70%
Performing Loans | Consumer loans | Consumer
Financing Receivable, Credit Quality Indicator [Line Items]
Amount	$ 84,422	$ 70,083
% of Total Loans	100.00%	100.00%
Non-Performing Loans
Financing Receivable, Credit Quality Indicator [Line Items]
Amount	$ 61,268	$ 50,422
% of Total Loans	0.30%	0.30%
Non-Performing Loans | Commercial loans
Financing Receivable, Credit Quality Indicator [Line Items]
Amount	$ 39,724	$ 34,644
% of Total Loans	0.30%	0.30%
Non-Performing Loans | Commercial loans | Multi-family
Financing Receivable, Credit Quality Indicator [Line Items]
Amount	$ 9,984	$ 5,127
% of Total Loans	0.20%	0.20%
Non-Performing Loans | Commercial loans | Commercial real estate
Financing Receivable, Credit Quality Indicator [Line Items]
Amount	$ 26,408	$ 23,435
% of Total Loans	0.70%	0.70%
Non-Performing Loans | Commercial loans | Commercial & industrial
Financing Receivable, Credit Quality Indicator [Line Items]
Amount	$ 2,138	$ 6,082
% of Total Loans	0.10%	0.30%
Non-Performing Loans | Commercial loans | Construction
Financing Receivable, Credit Quality Indicator [Line Items]
Amount	$ 1,120	$ 0
% of Total Loans	0.10%	0.00%
Non-Performing Loans | Commercial loans | Land - acquisition & development
Financing Receivable, Credit Quality Indicator [Line Items]
Amount	$ 74	$ 0
% of Total Loans	0.00%	0.00%
Non-Performing Loans | Consumer loans
Financing Receivable, Credit Quality Indicator [Line Items]
Amount	$ 21,544	$ 15,778
% of Total Loans	0.20%	0.20%
Non-Performing Loans | Consumer loans | Construction
Financing Receivable, Credit Quality Indicator [Line Items]
Amount	$ 88	$ 88
% of Total Loans	0.00%	0.00%
Non-Performing Loans | Consumer loans | Single-family residential
Financing Receivable, Credit Quality Indicator [Line Items]
Amount	$ 20,422	$ 14,918
% of Total Loans	0.20%	0.20%
Non-Performing Loans | Consumer loans | Land - consumer lot loans
Financing Receivable, Credit Quality Indicator [Line Items]
Amount	$ 236	$ 9
% of Total Loans	0.20%	0.00%
Non-Performing Loans | Consumer loans | HELOC
Financing Receivable, Credit Quality Indicator [Line Items]
Amount	$ 758	$ 736
% of Total Loans	0.30%	0.30%
Non-Performing Loans | Consumer loans | Consumer
Financing Receivable, Credit Quality Indicator [Line Items]
Amount	$ 40	$ 27
% of Total Loans	0.00%	0.00%