Allowance for Losses on Loans - Credit Risk Profile Based on Payment Activity (Details) - USD ($) $ in Thousands	Mar. 31, 2023	Sep. 30, 2022
Financing Receivable, Credit Quality Indicator [Line Items]
Gross loans	$ 17,449,326	$ 16,286,372
Commercial loans
Financing Receivable, Credit Quality Indicator [Line Items]
Gross loans	10,479,087	9,728,501
Commercial loans | Multi-family
Financing Receivable, Credit Quality Indicator [Line Items]
Gross loans	2,859,994	2,626,479
Commercial loans | Commercial real estate
Financing Receivable, Credit Quality Indicator [Line Items]
Gross loans	3,258,304	3,111,112
Commercial loans | Commercial & industrial
Financing Receivable, Credit Quality Indicator [Line Items]
Gross loans	2,585,196	2,343,403
Commercial loans | Construction
Financing Receivable, Credit Quality Indicator [Line Items]
Gross loans	1,608,513	1,423,891
Commercial loans | Land - acquisition & development
Financing Receivable, Credit Quality Indicator [Line Items]
Gross loans	167,080	223,616
Consumer loans
Financing Receivable, Credit Quality Indicator [Line Items]
Gross loans	6,970,239	6,557,871
Consumer loans | Construction
Financing Receivable, Credit Quality Indicator [Line Items]
Gross loans	403,783	397,343
Consumer loans | Single-family residential
Financing Receivable, Credit Quality Indicator [Line Items]
Gross loans	6,134,021	5,726,979
Consumer loans | Land - consumer lot loans
Financing Receivable, Credit Quality Indicator [Line Items]
Gross loans	140,140	151,945
Consumer loans | HELOC
Financing Receivable, Credit Quality Indicator [Line Items]
Gross loans	221,159	206,033
Consumer loans | Consumer
Financing Receivable, Credit Quality Indicator [Line Items]
Gross loans	71,136	75,571
Performing Loans
Financing Receivable, Credit Quality Indicator [Line Items]
Gross loans	$ 17,414,720	$ 16,251,838
% of Total Loans	99.80%	99.80%
Performing Loans | Commercial loans
Financing Receivable, Credit Quality Indicator [Line Items]
Gross loans	$ 10,461,043	$ 9,712,205
% of Total Loans	99.80%	99.90%
Performing Loans | Commercial loans | Multi-family
Financing Receivable, Credit Quality Indicator [Line Items]
Gross loans	$ 2,854,150	$ 2,620,567
% of Total Loans	99.80%	99.80%
Performing Loans | Commercial loans | Commercial real estate
Financing Receivable, Credit Quality Indicator [Line Items]
Gross loans	$ 3,253,785	$ 3,106,421
% of Total Loans	99.90%	99.80%
Performing Loans | Commercial loans | Commercial & industrial
Financing Receivable, Credit Quality Indicator [Line Items]
Gross loans	$ 2,577,515	$ 2,337,710
% of Total Loans	99.70%	99.80%
Performing Loans | Commercial loans | Construction
Financing Receivable, Credit Quality Indicator [Line Items]
Gross loans	$ 1,608,513	$ 1,423,891
% of Total Loans	100.00%	100.00%
Performing Loans | Commercial loans | Land - acquisition & development
Financing Receivable, Credit Quality Indicator [Line Items]
Gross loans	$ 167,080	$ 223,616
% of Total Loans	100.00%	100.00%
Performing Loans | Consumer loans
Financing Receivable, Credit Quality Indicator [Line Items]
Gross loans	$ 6,953,677	$ 6,539,633
% of Total Loans	99.80%	99.70%
Performing Loans | Consumer loans | Construction
Financing Receivable, Credit Quality Indicator [Line Items]
Gross loans	$ 403,783	$ 396,908
% of Total Loans	100.00%	99.90%
Performing Loans | Consumer loans | Single-family residential
Financing Receivable, Credit Quality Indicator [Line Items]
Gross loans	$ 6,117,625	$ 5,709,529
% of Total Loans	99.70%	99.70%
Performing Loans | Consumer loans | Land - consumer lot loans
Financing Receivable, Credit Quality Indicator [Line Items]
Gross loans	$ 140,134	$ 151,861
% of Total Loans	100.00%	99.90%
Performing Loans | Consumer loans | HELOC
Financing Receivable, Credit Quality Indicator [Line Items]
Gross loans	$ 221,031	$ 205,800
% of Total Loans	99.90%	99.90%
Performing Loans | Consumer loans | Consumer
Financing Receivable, Credit Quality Indicator [Line Items]
Gross loans	$ 71,104	$ 75,535
% of Total Loans	100.00%	100.00%
Non-Performing Loans
Financing Receivable, Credit Quality Indicator [Line Items]
Gross loans	$ 34,606	$ 34,534
% of Total Loans	0.20%	0.20%
Non-Performing Loans | Commercial loans
Financing Receivable, Credit Quality Indicator [Line Items]
Gross loans	$ 18,044	$ 16,296
% of Total Loans	0.20%	0.10%
Non-Performing Loans | Commercial loans | Multi-family
Financing Receivable, Credit Quality Indicator [Line Items]
Gross loans	$ 5,844	$ 5,912
% of Total Loans	0.20%	0.20%
Non-Performing Loans | Commercial loans | Commercial real estate
Financing Receivable, Credit Quality Indicator [Line Items]
Gross loans	$ 4,519	$ 4,691
% of Total Loans	0.10%	0.20%
Non-Performing Loans | Commercial loans | Commercial & industrial
Financing Receivable, Credit Quality Indicator [Line Items]
Gross loans	$ 7,681	$ 5,693
% of Total Loans	0.30%	0.20%
Non-Performing Loans | Commercial loans | Construction
Financing Receivable, Credit Quality Indicator [Line Items]
Gross loans	$ 0	$ 0
% of Total Loans	0.00%	0.00%
Non-Performing Loans | Commercial loans | Land - acquisition & development
Financing Receivable, Credit Quality Indicator [Line Items]
Gross loans	$ 0	$ 0
% of Total Loans	0.00%	0.00%
Non-Performing Loans | Consumer loans
Financing Receivable, Credit Quality Indicator [Line Items]
Gross loans	$ 16,562	$ 18,238
% of Total Loans	0.20%	0.40%
Non-Performing Loans | Consumer loans | Construction
Financing Receivable, Credit Quality Indicator [Line Items]
Gross loans	$ 0	$ 435
% of Total Loans	0.00%	0.10%
Non-Performing Loans | Consumer loans | Single-family residential
Financing Receivable, Credit Quality Indicator [Line Items]
Gross loans	$ 16,396	$ 17,450
% of Total Loans	0.30%	0.30%
Non-Performing Loans | Consumer loans | Land - consumer lot loans
Financing Receivable, Credit Quality Indicator [Line Items]
Gross loans	$ 6	$ 84
% of Total Loans	0.00%	0.10%
Non-Performing Loans | Consumer loans | HELOC
Financing Receivable, Credit Quality Indicator [Line Items]
Gross loans	$ 128	$ 233
% of Total Loans	0.10%	0.10%
Non-Performing Loans | Consumer loans | Consumer
Financing Receivable, Credit Quality Indicator [Line Items]
Gross loans	$ 32	$ 36
% of Total Loans	0.00%	0.00%