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Stock-Based Compensation - Schedule of Nonvested Restricted Stock Units Activity (Details) - shares
12 Months Ended
Sep. 30, 2024
Sep. 30, 2023
Sep. 30, 2022
Restricted Stock Units (RSUs) [Member]      
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]      
Award vesting period 2 years 2 years 2 years
Annual Equity Program [Member]      
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]      
Percentage Of Annual Performance Stock Grant Vests In Equal Quarterly Increments 50.00%    
Percentage Of Annual Performance Stock Grant Based On Achieving Specified Annual Performance Goals 50.00%    
Annual Equity Program [Member] | CEO      
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]      
Percentage Of Annual Performance Stock Grant Vests In Equal Quarterly Increments 40.00%    
Percentage Of Annual Performance Stock Grant Based On Achieving Specified Annual Performance Goals 60.00%    
Annual Equity Program [Member] | November 1, 2023 | Restricted Stock Units (RSUs) [Member]      
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]      
Equity Instruments Other than Options, Grants in Period 206,560    
Award vesting period 3 years    
Annual Equity Program [Member] | November 1, 2022 | Restricted Stock Units (RSUs) [Member]      
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]      
Equity Instruments Other than Options, Grants in Period 240,808    
Award vesting period 3 years    
Annual Equity Program [Member] | November 1, 2021 [Member] | Restricted Stock Units (RSUs) [Member]      
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]      
Equity Instruments Other than Options, Grants in Period 160,384    
Award vesting period 3 years    
Annual Equity Program [Member] | November 2, 2020 | Restricted Stock Units (RSUs) [Member]      
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]      
Equity Instruments Other than Options, Grants in Period 257,568    
Award vesting period 3 years