Segment Information (Details) $ in Thousands	3 Months Ended		6 Months Ended
	Mar. 31, 2025 USD ($) region state	Mar. 31, 2024 USD ($)	Mar. 31, 2025 USD ($) region state segment	Mar. 31, 2024 USD ($)	Sep. 30, 2024 USD ($)
Segment Reporting Information [Line Items]
Number of states in which home building segments operate | state	13		13
Number of regions in which entity operates | region	3		3
Number of reportable segments | segment			3
Revenue	$ 565,339	$ 541,540	$ 1,034,292	$ 928,358
Operating income	13,369	35,991	15,507	56,256
Depreciation and amortization	4,647	3,573	8,702	5,806
Capital expenditures			13,061	11,501
Assets	2,654,745		2,654,745		$ 2,591,527
Operating Segments
Segment Reporting Information [Line Items]
Operating income	50,769	69,265	87,476	113,100
Depreciation and amortization	3,463	3,126	6,408	4,966
Corporate and unallocated
Segment Reporting Information [Line Items]
Operating income	(37,400)	(33,274)	(71,969)	(56,844)
Depreciation and amortization	1,184	447	2,294	840
Capital expenditures			4,280	3,301
Assets	502,632		502,632		633,764
West
Segment Reporting Information [Line Items]
Revenue	373,856	347,338	672,772	584,431
West | Operating Segments
Segment Reporting Information [Line Items]
Operating income	39,475	46,030	66,889	74,369
Depreciation and amortization	2,518	2,452	4,709	3,763
Capital expenditures			5,012	6,873
Assets	1,185,797		1,185,797		1,114,450
East
Segment Reporting Information [Line Items]
Revenue	120,856	111,844	230,738	186,621
East | Operating Segments
Segment Reporting Information [Line Items]
Operating income	7,557	12,282	14,229	18,638
Depreciation and amortization	548	406	1,004	615
Capital expenditures			1,211	865
Assets	519,202		519,202		454,255
Southeast
Segment Reporting Information [Line Items]
Revenue	70,627	82,358	130,782	157,306
Southeast | Operating Segments
Segment Reporting Information [Line Items]
Operating income	3,737	10,953	6,358	20,093
Depreciation and amortization	397	$ 268	695	588
Capital expenditures			2,558	$ 462
Assets	$ 447,114		$ 447,114		$ 389,058