Segment Information - Schedule of Financial Information About Reportable Segments and Corporate and Unallocated (Details) - USD ($) $ in Thousands	3 Months Ended		6 Months Ended
	Mar. 31, 2026	Mar. 31, 2025	Mar. 31, 2026	Mar. 31, 2025
Segment Reporting Information [Line Items]
Revenue	$ 409,846	$ 565,339	$ 773,337	$ 1,034,292
Home construction and land sale expenses	359,851	478,813	683,768	875,688
Inventory impairments and abandonments	1,295	528	3,665	528
Commissions	13,390	18,783	25,406	34,896
Sales and marketing	18,593	16,127	37,870	31,040
Other general and administrative expenses	31,601	33,072	65,313	67,931
Depreciation and amortization	4,084	4,647	8,126	8,702
Operating income (loss)	(18,968)	13,369	(50,811)	15,507
Other income, net	433	799	1,211	1,827
Loss before income taxes	(18,535)	14,168	(49,600)	17,334
Operating Segments
Segment Reporting Information [Line Items]
Revenue	409,846	565,339	773,337	1,034,292
Home construction and land sale expenses	347,589	463,811	658,991	851,327
Inventory impairments and abandonments	1,174	528	3,422	528
Commissions	13,390	18,783	25,406	34,896
Sales and marketing	14,659	12,530	28,662	24,458
Other general and administrative expenses	15,556	15,455	28,983	29,199
Depreciation and amortization	2,537	3,463	5,206	6,408
Operating income (loss)	14,941	50,769	22,667	87,476
Operating Segments | West
Segment Reporting Information [Line Items]
Revenue	236,856	373,856	460,360	672,772
Home construction and land sale expenses	201,711	301,889	393,889	545,798
Inventory impairments and abandonments	1,174	528	2,523	528
Commissions	8,324	12,545	16,047	23,107
Sales and marketing	8,845	7,894	17,559	15,140
Other general and administrative expenses	9,049	9,007	16,610	16,601
Depreciation and amortization	1,678	2,518	3,476	4,709
Operating income (loss)	6,075	39,475	10,256	66,889
Operating Segments | East
Segment Reporting Information [Line Items]
Revenue	97,125	120,856	190,584	230,738
Home construction and land sale expenses	83,053	102,885	162,572	196,100
Inventory impairments and abandonments	0	0	899	0
Commissions	2,522	3,773	5,119	7,193
Sales and marketing	3,235	2,719	6,372	5,402
Other general and administrative expenses	3,660	3,374	6,959	6,810
Depreciation and amortization	328	548	803	1,004
Operating income (loss)	4,327	7,557	7,860	14,229
Operating Segments | Southeast
Segment Reporting Information [Line Items]
Revenue	75,865	70,627	122,393	130,782
Home construction and land sale expenses	62,825	59,037	102,530	109,429
Inventory impairments and abandonments	0	0	0	0
Commissions	2,544	2,465	4,240	4,596
Sales and marketing	2,579	1,917	4,731	3,916
Other general and administrative expenses	2,847	3,074	5,414	5,788
Depreciation and amortization	531	397	927	695
Operating income (loss)	4,539	3,737	4,551	6,358
Corporate and unallocated
Segment Reporting Information [Line Items]
Revenue	0	0	0	0
Home construction and land sale expenses	12,262	15,002	24,777	24,361
Inventory impairments and abandonments	121	0	243	0
Commissions	0	0	0	0
Sales and marketing	3,934	3,597	9,208	6,582
Other general and administrative expenses	16,045	17,617	36,330	38,732
Depreciation and amortization	1,547	1,184	2,920	2,294
Operating income (loss)	$ (33,909)	$ (37,400)	$ (73,478)	$ (71,969)