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Property and Equipment, net - Narrative (Details) - USD ($)
$ in Millions
12 Months Ended
Sep. 30, 2024
Sep. 30, 2023
Sep. 30, 2022
Property, Plant and Equipment [Line Items]      
Depreciation expense $ 45.6 $ 36.3 $ 30.0
Capitalized computer software, additions 36.1 $ 29.9  
Write off of property and equipment assets $ 4.8    
Minimum      
Property, Plant and Equipment [Line Items]      
Property plant and equipment, useful life 3 years    
Maximum      
Property, Plant and Equipment [Line Items]      
Property plant and equipment, useful life 10 years