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Allowance for Losses on Loans - Credit Risk Profile Based on Payment Activity (Details) - USD ($) $ in Thousands	Mar. 31, 2022	Sep. 30, 2021
Financing Receivable, Credit Quality Indicator [Line Items]
Amount	$ 15,266,310	$ 14,004,870
Commercial loans
Financing Receivable, Credit Quality Indicator [Line Items]
Amount	9,106,457	8,316,591
Commercial loans | Multi-family
Financing Receivable, Credit Quality Indicator [Line Items]
Amount	2,377,657	2,273,689
Commercial loans | Commercial real estate
Financing Receivable, Credit Quality Indicator [Line Items]
Amount	2,808,628	2,429,332
Commercial loans | Commercial & industrial
Financing Receivable, Credit Quality Indicator [Line Items]
Amount	2,497,008	2,303,927
Commercial loans | Construction
Financing Receivable, Credit Quality Indicator [Line Items]
Amount	1,212,103	1,117,227
Commercial loans | Land - acquisition & development
Financing Receivable, Credit Quality Indicator [Line Items]
Amount	211,061	192,416
Consumer loans
Financing Receivable, Credit Quality Indicator [Line Items]
Amount	6,159,853	5,688,279
Consumer loans | Construction
Financing Receivable, Credit Quality Indicator [Line Items]
Amount	344,113	347,752
Consumer loans | Single-family residential
Financing Receivable, Credit Quality Indicator [Line Items]
Amount	5,418,645	4,937,064
Consumer loans | Land - consumer lot loans
Financing Receivable, Credit Quality Indicator [Line Items]
Amount	153,549	148,534
Consumer loans | HELOC
Financing Receivable, Credit Quality Indicator [Line Items]
Amount	175,929	166,940
Consumer loans | Consumer
Financing Receivable, Credit Quality Indicator [Line Items]
Amount	67,617	87,989
Performing Loans
Financing Receivable, Credit Quality Indicator [Line Items]
Amount	$ 15,232,671	$ 13,973,121
% of Total Loans	99.80%	99.80%
Performing Loans | Commercial loans
Financing Receivable, Credit Quality Indicator [Line Items]
Amount	$ 9,092,573	$ 8,304,868
% of Total Loans	99.80%	99.90%
Performing Loans | Commercial loans | Multi-family
Financing Receivable, Credit Quality Indicator [Line Items]
Amount	$ 2,377,657	$ 2,273,214
% of Total Loans	100.00%	100.00%
Performing Loans | Commercial loans | Commercial real estate
Financing Receivable, Credit Quality Indicator [Line Items]
Amount	$ 2,802,216	$ 2,421,294
% of Total Loans	99.80%	99.70%
Performing Loans | Commercial loans | Commercial & industrial
Financing Receivable, Credit Quality Indicator [Line Items]
Amount	$ 2,492,219	$ 2,303,562
% of Total Loans	99.80%	100.00%
Performing Loans | Commercial loans | Construction
Financing Receivable, Credit Quality Indicator [Line Items]
Amount	$ 1,211,760	$ 1,116,722
% of Total Loans	100.00%	100.00%
Performing Loans | Commercial loans | Land - acquisition & development
Financing Receivable, Credit Quality Indicator [Line Items]
Amount	$ 208,721	$ 190,076
% of Total Loans	98.90%	98.80%
Performing Loans | Consumer loans
Financing Receivable, Credit Quality Indicator [Line Items]
Amount	$ 6,140,098	$ 5,668,253
% of Total Loans	99.70%	99.60%
Performing Loans | Consumer loans | Construction
Financing Receivable, Credit Quality Indicator [Line Items]
Amount	$ 343,648	$ 347,752
% of Total Loans	99.90%	100.00%
Performing Loans | Consumer loans | Single-family residential
Financing Receivable, Credit Quality Indicator [Line Items]
Amount	$ 5,400,033	$ 4,917,744
% of Total Loans	99.70%	99.60%
Performing Loans | Consumer loans | Land - consumer lot loans
Financing Receivable, Credit Quality Indicator [Line Items]
Amount	$ 153,239	$ 148,175
% of Total Loans	99.80%	99.80%
Performing Loans | Consumer loans | HELOC
Financing Receivable, Credit Quality Indicator [Line Items]
Amount	$ 175,600	$ 166,653
% of Total Loans	99.80%	99.80%
Performing Loans | Consumer loans | Consumer
Financing Receivable, Credit Quality Indicator [Line Items]
Amount	$ 67,578	$ 87,929
% of Total Loans	99.90%	99.90%
Non-Performing Loans
Financing Receivable, Credit Quality Indicator [Line Items]
Amount	$ 33,639	$ 31,749
% of Total Loans	0.20%	0.20%
Non-Performing Loans | Commercial loans
Financing Receivable, Credit Quality Indicator [Line Items]
Amount	$ 13,884	$ 11,723
% of Total Loans	0.20%	0.10%
Non-Performing Loans | Commercial loans | Multi-family
Financing Receivable, Credit Quality Indicator [Line Items]
Amount	$ 0	$ 475
% of Total Loans	0.00%	0.00%
Non-Performing Loans | Commercial loans | Commercial real estate
Financing Receivable, Credit Quality Indicator [Line Items]
Amount	$ 6,412	$ 8,038
% of Total Loans	0.20%	0.30%
Non-Performing Loans | Commercial loans | Commercial & industrial
Financing Receivable, Credit Quality Indicator [Line Items]
Amount	$ 4,789	$ 365
% of Total Loans	0.20%	0.00%
Non-Performing Loans | Commercial loans | Construction
Financing Receivable, Credit Quality Indicator [Line Items]
Amount	$ 343	$ 505
% of Total Loans	0.00%	0.00%
Non-Performing Loans | Commercial loans | Land - acquisition & development
Financing Receivable, Credit Quality Indicator [Line Items]
Amount	$ 2,340	$ 2,340
% of Total Loans	1.10%	1.20%
Non-Performing Loans | Consumer loans
Financing Receivable, Credit Quality Indicator [Line Items]
Amount	$ 19,755	$ 20,026
% of Total Loans	0.30%	0.40%
Non-Performing Loans | Consumer loans | Construction
Financing Receivable, Credit Quality Indicator [Line Items]
Amount	$ 465	$ 0
% of Total Loans	0.10%	0.00%
Non-Performing Loans | Consumer loans | Single-family residential
Financing Receivable, Credit Quality Indicator [Line Items]
Amount	$ 18,612	$ 19,320
% of Total Loans	0.30%	0.40%
Non-Performing Loans | Consumer loans | Land - consumer lot loans
Financing Receivable, Credit Quality Indicator [Line Items]
Amount	$ 310	$ 359
% of Total Loans	0.20%	0.20%
Non-Performing Loans | Consumer loans | HELOC
Financing Receivable, Credit Quality Indicator [Line Items]
Amount	$ 329	$ 287
% of Total Loans	0.20%	0.20%
Non-Performing Loans | Consumer loans | Consumer
Financing Receivable, Credit Quality Indicator [Line Items]
Amount	$ 39	$ 60
% of Total Loans	0.10%	0.10%

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