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Property and Equipment, net - Narrative (Details) - USD ($)
$ in Millions
12 Months Ended
Sep. 30, 2023
Sep. 30, 2022
Sep. 30, 2021
Property, Plant and Equipment [Line Items]      
Depreciation expense $ 36.3 $ 30.0 $ 21.3
Capitalized computer software, additions $ 29.9 $ 24.8  
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