Summary of Significant Accounting Policies - Advertising Costs (Details) - USD ($) $ in Millions	12 Months Ended
Sep. 30, 2024	Sep. 30, 2023	Sep. 30, 2022
Accounting Policies [Abstract]
Advertising cost	$ 26.9	$ 24.8	$ 13.4
Net of related co-op assistance	$ 1.6	$ 2.2	$ 1.8

Amount charged to advertising expense for the period, which are expenses incurred with the objective of increasing revenue for a specified brand, product or product line.

Reference 1: http://www.xbrl.org/2003/role/exampleRef
-Topic 720
-SubTopic 35
-Name Accounting Standards Codification
-Section 55
-Paragraph 1
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147483385/720-35-55-1

Reference 2: http://www.xbrl.org/2003/role/disclosureRef
-Topic 720
-SubTopic 35
-Name Accounting Standards Codification
-Section 50
-Paragraph 1
-Subparagraph (b)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147483406/720-35-50-1

Name:	us-gaap_AdvertisingExpense
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	duration