Securities (Amortized Cost, Estimated Fair Value, and Gross Unrealized Gains and Losses of AFS and HTM Securities) (Details) - USD ($) $ in Thousands	Dec. 31, 2023	Sep. 30, 2023
Marketable Securities [Line Items]
Available-for-sale Securities, Amortized Cost	$ 721,612	$ 1,385,992
Available-for-sale Securities, Gross Unrealized Gains	19,657	113
Available-for-sale Securities, Gross Unrealized Losses	807	1,623
Available-for-sale Securities, Estimated Fair Value	740,462	1,384,482
MBS [Member]
Marketable Securities [Line Items]
Available-for-sale Securities, Amortized Cost	503,912	901,440
Available-for-sale Securities, Gross Unrealized Gains	19,599	113
Available-for-sale Securities, Gross Unrealized Losses	291	819
Available-for-sale Securities, Estimated Fair Value	523,220	900,734
US Treasury Bills [Member]
Marketable Securities [Line Items]
Available-for-sale Securities, Amortized Cost	213,700
Available-for-sale Securities, Gross Unrealized Gains	58
Available-for-sale Securities, Gross Unrealized Losses	0
Available-for-sale Securities, Estimated Fair Value	213,758
GSE Debentures [Member]
Marketable Securities [Line Items]
Available-for-sale Securities, Amortized Cost		479,610
Available-for-sale Securities, Gross Unrealized Gains		0
Available-for-sale Securities, Gross Unrealized Losses		182
Available-for-sale Securities, Estimated Fair Value		479,428
Corporate Bonds [Member]
Marketable Securities [Line Items]
Available-for-sale Securities, Amortized Cost	4,000	4,000
Available-for-sale Securities, Gross Unrealized Gains	0	0
Available-for-sale Securities, Gross Unrealized Losses	516	622
Available-for-sale Securities, Estimated Fair Value	$ 3,484	3,378
Municipal Bonds [Member]
Marketable Securities [Line Items]
Available-for-sale Securities, Amortized Cost		942
Available-for-sale Securities, Gross Unrealized Gains		0
Available-for-sale Securities, Gross Unrealized Losses		0
Available-for-sale Securities, Estimated Fair Value		$ 942

Amount, before tax, of unrealized gain in accumulated other comprehensive income (AOCI) on investment in debt security measured at fair value with change in fair value recognized in other comprehensive income (available-for-sale).

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Topic 320
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 2
-Subparagraph (b)
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147481800/320-10-50-2

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- Definition

Amount, before tax, of unrealized loss in accumulated other comprehensive income (AOCI) on investment in debt security measured at fair value with change in fair value recognized in other comprehensive income (available-for-sale).

+ References

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Topic 320
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 2
-Subparagraph (c)
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147481800/320-10-50-2

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Amortized cost excluding accrued interest, after allowance for credit loss, of investment in debt security measured at fair value with change in fair value recognized in other comprehensive income (available-for-sale).

+ References

Reference 1: http://www.xbrl.org/2009/role/commonPracticeRef
-Topic 326
-SubTopic 30
-Name Accounting Standards Codification
-Section 45
-Paragraph 1
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147479130/326-30-45-1

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Amount excluding accrued interest, of investment in debt security measured at fair value with change in fair value recognized in other comprehensive income (available-for-sale).

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