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Allowance for Losses on Loans - Internally Assigned Grade (Details) - USD ($) $ in Thousands	9 Months Ended	12 Months Ended
	Jun. 30, 2023	Sep. 30, 2022
Financing Receivable, Credit Quality Indicator [Line Items]
Gross loans	$ 17,562,257	$ 16,286,372
Pass
Financing Receivable, Credit Quality Indicator [Line Items]
Gross loans	$ 17,140,731	$ 16,045,127
Pass | Accounts Receivable | Credit Concentration Risk
Financing Receivable, Credit Quality Indicator [Line Items]
Total grade as a % of total loans	97.60%	98.52%
Special mention
Financing Receivable, Credit Quality Indicator [Line Items]
Gross loans	$ 124,979	$ 33,250
Special mention | Accounts Receivable | Credit Concentration Risk
Financing Receivable, Credit Quality Indicator [Line Items]
Total grade as a % of total loans	0.71%	0.20%
Substandard
Financing Receivable, Credit Quality Indicator [Line Items]
Gross loans	$ 296,547	$ 207,995
Substandard | Accounts Receivable | Credit Concentration Risk
Financing Receivable, Credit Quality Indicator [Line Items]
Total grade as a % of total loans	1.69%	1.28%
Doubtful
Financing Receivable, Credit Quality Indicator [Line Items]
Gross loans	$ 0	$ 0
Doubtful | Accounts Receivable | Credit Concentration Risk
Financing Receivable, Credit Quality Indicator [Line Items]
Total grade as a % of total loans	0.00%	0.00%
Loss
Financing Receivable, Credit Quality Indicator [Line Items]
Gross loans	$ 0	$ 0
Loss | Accounts Receivable | Credit Concentration Risk
Financing Receivable, Credit Quality Indicator [Line Items]
Total grade as a % of total loans	0.00%	0.00%
Commercial loans
Financing Receivable, Credit Quality Indicator [Line Items]
Gross loans	$ 10,488,716	$ 9,728,501
Commercial loans | Pass
Financing Receivable, Credit Quality Indicator [Line Items]
Gross loans	10,087,008	9,508,927
Commercial loans | Special mention
Financing Receivable, Credit Quality Indicator [Line Items]
Gross loans	124,979	33,250
Commercial loans | Substandard
Financing Receivable, Credit Quality Indicator [Line Items]
Gross loans	276,729	186,324
Commercial loans | Doubtful
Financing Receivable, Credit Quality Indicator [Line Items]
Gross loans	0	0
Commercial loans | Loss
Financing Receivable, Credit Quality Indicator [Line Items]
Gross loans	0	0
Commercial loans | Multi-family
Financing Receivable, Credit Quality Indicator [Line Items]
Gross loans	2,858,433	2,626,479
Commercial loans | Multi-family | Pass
Financing Receivable, Credit Quality Indicator [Line Items]
Gross loans	2,749,291	2,612,669
Commercial loans | Multi-family | Special mention
Financing Receivable, Credit Quality Indicator [Line Items]
Gross loans	90,187	0
Commercial loans | Multi-family | Substandard
Financing Receivable, Credit Quality Indicator [Line Items]
Gross loans	18,955	13,810
Commercial loans | Multi-family | Doubtful
Financing Receivable, Credit Quality Indicator [Line Items]
Gross loans	0	0
Commercial loans | Multi-family | Loss
Financing Receivable, Credit Quality Indicator [Line Items]
Gross loans	0	0
Commercial loans | Commercial real estate
Financing Receivable, Credit Quality Indicator [Line Items]
Gross loans	3,218,451	3,111,112
Commercial loans | Commercial real estate | Pass
Financing Receivable, Credit Quality Indicator [Line Items]
Gross loans	3,114,517	3,054,241
Commercial loans | Commercial real estate | Special mention
Financing Receivable, Credit Quality Indicator [Line Items]
Gross loans	23,238	1,594
Commercial loans | Commercial real estate | Substandard
Financing Receivable, Credit Quality Indicator [Line Items]
Gross loans	80,696	55,277
Commercial loans | Commercial real estate | Doubtful
Financing Receivable, Credit Quality Indicator [Line Items]
Gross loans	0	0
Commercial loans | Commercial real estate | Loss
Financing Receivable, Credit Quality Indicator [Line Items]
Gross loans	0	0
Commercial loans | Commercial & industrial
Financing Receivable, Credit Quality Indicator [Line Items]
Gross loans	2,490,740	2,343,403
Commercial loans | Commercial & industrial | Pass
Financing Receivable, Credit Quality Indicator [Line Items]
Gross loans	2,329,675	2,196,767
Commercial loans | Commercial & industrial | Special mention
Financing Receivable, Credit Quality Indicator [Line Items]
Gross loans	6,815	31,656
Commercial loans | Commercial & industrial | Substandard
Financing Receivable, Credit Quality Indicator [Line Items]
Gross loans	154,250	114,980
Commercial loans | Commercial & industrial | Doubtful
Financing Receivable, Credit Quality Indicator [Line Items]
Gross loans	0	0
Commercial loans | Commercial & industrial | Loss
Financing Receivable, Credit Quality Indicator [Line Items]
Gross loans	0	0
Commercial loans | Construction
Financing Receivable, Credit Quality Indicator [Line Items]
Gross loans	1,759,434	1,423,891
Commercial loans | Construction | Pass
Financing Receivable, Credit Quality Indicator [Line Items]
Gross loans	1,732,137	1,421,634
Commercial loans | Construction | Special mention
Financing Receivable, Credit Quality Indicator [Line Items]
Gross loans	4,739	0
Commercial loans | Construction | Substandard
Financing Receivable, Credit Quality Indicator [Line Items]
Gross loans	22,558	2,257
Commercial loans | Construction | Doubtful
Financing Receivable, Credit Quality Indicator [Line Items]
Gross loans	0	0
Commercial loans | Construction | Loss
Financing Receivable, Credit Quality Indicator [Line Items]
Gross loans	0	0
Commercial loans | Land - acquisition & development
Financing Receivable, Credit Quality Indicator [Line Items]
Gross loans	161,658	223,616
Commercial loans | Land - acquisition & development | Pass
Financing Receivable, Credit Quality Indicator [Line Items]
Gross loans	161,388	223,616
Commercial loans | Land - acquisition & development | Special mention
Financing Receivable, Credit Quality Indicator [Line Items]
Gross loans	0	0
Commercial loans | Land - acquisition & development | Substandard
Financing Receivable, Credit Quality Indicator [Line Items]
Gross loans	270	0
Commercial loans | Land - acquisition & development | Doubtful
Financing Receivable, Credit Quality Indicator [Line Items]
Gross loans	0	0
Commercial loans | Land - acquisition & development | Loss
Financing Receivable, Credit Quality Indicator [Line Items]
Gross loans	0	0
Consumer loans
Financing Receivable, Credit Quality Indicator [Line Items]
Gross loans	7,073,541	6,557,871
Consumer loans | Pass
Financing Receivable, Credit Quality Indicator [Line Items]
Gross loans	7,053,723	6,536,200
Consumer loans | Special mention
Financing Receivable, Credit Quality Indicator [Line Items]
Gross loans	0	0
Consumer loans | Substandard
Financing Receivable, Credit Quality Indicator [Line Items]
Gross loans	19,818	21,671
Consumer loans | Doubtful
Financing Receivable, Credit Quality Indicator [Line Items]
Gross loans	0	0
Consumer loans | Loss
Financing Receivable, Credit Quality Indicator [Line Items]
Gross loans	0	0
Consumer loans | Construction
Financing Receivable, Credit Quality Indicator [Line Items]
Gross loans	376,045	397,343
Consumer loans | Construction | Pass
Financing Receivable, Credit Quality Indicator [Line Items]
Gross loans	375,957	396,908
Consumer loans | Construction | Special mention
Financing Receivable, Credit Quality Indicator [Line Items]
Gross loans	0	0
Consumer loans | Construction | Substandard
Financing Receivable, Credit Quality Indicator [Line Items]
Gross loans	88	435
Consumer loans | Construction | Doubtful
Financing Receivable, Credit Quality Indicator [Line Items]
Gross loans	0	0
Consumer loans | Construction | Loss
Financing Receivable, Credit Quality Indicator [Line Items]
Gross loans	0	0
Consumer loans | Single-family residential
Financing Receivable, Credit Quality Indicator [Line Items]
Gross loans	6,258,592	5,726,979
Consumer loans | Single-family residential | Pass
Financing Receivable, Credit Quality Indicator [Line Items]
Gross loans	6,239,912	5,706,199
Consumer loans | Single-family residential | Special mention
Financing Receivable, Credit Quality Indicator [Line Items]
Gross loans	0	0
Consumer loans | Single-family residential | Substandard
Financing Receivable, Credit Quality Indicator [Line Items]
Gross loans	18,680	20,780
Consumer loans | Single-family residential | Doubtful
Financing Receivable, Credit Quality Indicator [Line Items]
Gross loans	0	0
Consumer loans | Single-family residential | Loss
Financing Receivable, Credit Quality Indicator [Line Items]
Gross loans	0	0
Consumer loans | Land - consumer lot loans
Financing Receivable, Credit Quality Indicator [Line Items]
Gross loans	133,994	151,945
Consumer loans | Land - consumer lot loans | Pass
Financing Receivable, Credit Quality Indicator [Line Items]
Gross loans	133,758	151,723
Consumer loans | Land - consumer lot loans | Special mention
Financing Receivable, Credit Quality Indicator [Line Items]
Gross loans	0	0
Consumer loans | Land - consumer lot loans | Substandard
Financing Receivable, Credit Quality Indicator [Line Items]
Gross loans	236	222
Consumer loans | Land - consumer lot loans | Doubtful
Financing Receivable, Credit Quality Indicator [Line Items]
Gross loans	0	0
Consumer loans | Land - consumer lot loans | Loss
Financing Receivable, Credit Quality Indicator [Line Items]
Gross loans	0	0
Consumer loans | HELOC
Financing Receivable, Credit Quality Indicator [Line Items]
Gross loans	228,132	206,033
Consumer loans | HELOC | Pass
Financing Receivable, Credit Quality Indicator [Line Items]
Gross loans	227,331	205,800
Consumer loans | HELOC | Special mention
Financing Receivable, Credit Quality Indicator [Line Items]
Gross loans	0	0
Consumer loans | HELOC | Substandard
Financing Receivable, Credit Quality Indicator [Line Items]
Gross loans	801	233
Consumer loans | HELOC | Doubtful
Financing Receivable, Credit Quality Indicator [Line Items]
Gross loans	0	0
Consumer loans | HELOC | Loss
Financing Receivable, Credit Quality Indicator [Line Items]
Gross loans	0	0
Consumer loans | Consumer
Financing Receivable, Credit Quality Indicator [Line Items]
Gross loans	76,778	75,571
Consumer loans | Consumer | Pass
Financing Receivable, Credit Quality Indicator [Line Items]
Gross loans	76,765	75,570
Consumer loans | Consumer | Special mention
Financing Receivable, Credit Quality Indicator [Line Items]
Gross loans	0	0
Consumer loans | Consumer | Substandard
Financing Receivable, Credit Quality Indicator [Line Items]
Gross loans	13	1
Consumer loans | Consumer | Doubtful
Financing Receivable, Credit Quality Indicator [Line Items]
Gross loans	0	0
Consumer loans | Consumer | Loss
Financing Receivable, Credit Quality Indicator [Line Items]
Gross loans	$ 0	$ 0

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