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Stock-Based Compensation - Additional Disclosures (Details) - USD ($)
$ / shares in Units, $ in Thousands
9 Months Ended 12 Months Ended
Jun. 30, 2022
Jun. 30, 2021
Jun. 30, 2022
Sep. 30, 2021
Sep. 30, 2020
May 17, 2022
May 16, 2022
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]              
Issuance of shares of common stock $ 5,702 $ 0   $ 0 $ 0    
Payments related to tax withholding $ 1,676 $ 0   0 0    
Common stock reserved for future issuance or settlement (in shares) 4,400,000   4,400,000        
Share-based Payment Arrangement, Expense $ 15,763     1,744 606    
Post-combination portion              
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]              
Share-based Compensation Arrangement by Share-based Payment Award, Options, Outstanding, Number           96,650  
Pre-combination portion              
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]              
Share-based Compensation Arrangement by Share-based Payment Award, Options, Outstanding, Number             102,305
Emerson stock-based compensation plans              
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]              
Share-based Payment Arrangement, Expense 1,100     $ 1,700 $ 600    
Restricted Stock Units              
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]              
Granted (in dollars per share)     $ 193.70        
Total fair value of shares vested from RSU grants     $ 46,600        
Total unrecognized compensation cost 69,500   $ 69,500        
Total unrecognized compensation cost, period of recognition     2 years 9 months 7 days        
Share-based Compensation Arrangement by Share-based Payment Award, Options, Outstanding, Number             504,386
Restricted Stock Units | Restricted Stock Units              
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]              
Share-based Compensation Arrangement by Share-based Payment Award, Options, Outstanding, Number           453,397  
Restricted Stock Units | Post-combination portion              
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]              
Share-based Compensation Arrangement by Share-based Payment Award, Options, Outstanding, Number           61,898  
Restricted Stock Units | Pre-combination portion              
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]              
Share-based Compensation Arrangement by Share-based Payment Award, Options, Outstanding, Number             22,422
Restricted Stock Units | Emerson stock-based compensation plans              
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]              
Granted (in dollars per share)     $ 166.30        
Share-based Payment Arrangement, Option [Member]              
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]              
Total unrecognized compensation cost $ 35,300   $ 35,300        
Total unrecognized compensation cost, period of recognition     2 years 4 months 9 days        
Granted (in dollars per share)     $ 193.55        
Total intrinsic value of options exercised     $ 18,700        
Issuance of shares of common stock     23,000        
Payments related to tax withholding     $ 16,000        
Share-based Compensation Arrangement by Share-based Payment Award, Options, Outstanding, Number 1,175,853   1,175,853 0     1,326,860
Share-based Payment Arrangement, Option [Member] | Share-based Payment Arrangement, Option [Member]              
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]              
Share-based Compensation Arrangement by Share-based Payment Award, Options, Outstanding, Number           1,165,494  
Share-based Payment Arrangement, Option [Member] | Post-combination portion              
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]              
Share-based Compensation Arrangement by Share-based Payment Award, Options, Outstanding, Number           34,752  
Share-based Payment Arrangement, Option [Member] | Pre-combination portion              
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]              
Share-based Compensation Arrangement by Share-based Payment Award, Options, Outstanding, Number             79,883
Share-based Payment Arrangement, Option [Member] | Emerson stock-based compensation plans              
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]              
Granted (in dollars per share)     $ 101.44