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Share-Based Compensation - Additional Information (Details) - USD ($)
$ in Thousands
3 Months Ended 9 Months Ended
Sep. 30, 2022
Sep. 30, 2021
Sep. 30, 2022
Sep. 30, 2021
Share Based Compensation Arrangement By Share Based Payment Award [Line Items]        
Unrecognized pre-tax noncash compensation $ 36,700   $ 36,700  
Allocated share based compensation expense 2,022 $ 1,343 $ 5,824 $ 4,569
Expected weighted average period     3 years 1 month 6 days  
Employee stock purchase plan expenses 100   $ 300  
Cost of Services [Member]        
Share Based Compensation Arrangement By Share Based Payment Award [Line Items]        
Allocated share based compensation expense 292 3 842 76
Selling, General and Administrative Expenses [Member]        
Share Based Compensation Arrangement By Share Based Payment Award [Line Items]        
Allocated share based compensation expense 1,328 1,285 4,064 4,317
Product and Technology Expense [Member]        
Share Based Compensation Arrangement By Share Based Payment Award [Line Items]        
Allocated share based compensation expense $ 402 $ 55 $ 918 $ 176
Maximum        
Share Based Compensation Arrangement By Share Based Payment Award [Line Items]        
ESPP percentage     15.00%  
IPO [Member] | Minimum        
Share Based Compensation Arrangement By Share Based Payment Award [Line Items]        
Vesting period     4 years  
IPO [Member] | Maximum        
Share Based Compensation Arrangement By Share Based Payment Award [Line Items]        
Vesting period     5 years  
2021 Equity Plan [Member]        
Share Based Compensation Arrangement By Share Based Payment Award [Line Items]        
Stock options plan expiration period     10 years  
Common stock, reserved for future issuance   17,525,000   17,525,000
Share available for issuance 13,578,273   13,578,273  
Successor Plan        
Share Based Compensation Arrangement By Share Based Payment Award [Line Items]        
Stock options plan expiration period     10 years  
Number of units, issued       0
Share-based Payment Arrangement, Option        
Share Based Compensation Arrangement By Share Based Payment Award [Line Items]        
Vesting percentage     50.00%  
Vesting period     5 years  
Unrecognized pre-tax noncash compensation $ 21,800   $ 21,800  
Share-based Payment Arrangement, Option | Share-based Payment Arrangement, Tranche One | 2021 Equity Plan [Member]        
Share Based Compensation Arrangement By Share Based Payment Award [Line Items]        
Vesting percentage     20.00%  
Vesting period     5 years  
Share-based Payment Arrangement, Option | Successor Plan        
Share Based Compensation Arrangement By Share Based Payment Award [Line Items]        
Vesting percentage     50.00%  
Share-based Payment Arrangement, Option | Successor Plan | Share-based Payment Arrangement, Tranche One        
Share Based Compensation Arrangement By Share Based Payment Award [Line Items]        
Vesting percentage     20.00%  
Vesting period     5 years  
Share-based Payment Arrangement, Option | Successor Plan | Share-based Payment Arrangement, Tranche Two        
Share Based Compensation Arrangement By Share Based Payment Award [Line Items]        
Vesting period     5 years  
Restricted Stock Agreements [Member]        
Share Based Compensation Arrangement By Share Based Payment Award [Line Items]        
Unrecognized pre-tax noncash compensation 7,900   $ 7,900  
Restricted Stock Units [Member]        
Share Based Compensation Arrangement By Share Based Payment Award [Line Items]        
Unrecognized pre-tax noncash compensation $ 7,000   $ 7,000