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Share-Based Compensation - Additional Information (Details) - USD ($)
$ in Thousands
1 Months Ended 3 Months Ended 8 Months Ended 9 Months Ended 11 Months Ended 12 Months Ended
Jan. 31, 2020
Sep. 30, 2021
Sep. 30, 2020
Sep. 30, 2020
Sep. 30, 2021
Dec. 31, 2020
Dec. 31, 2019
Share Based Compensation Arrangement By Share Based Payment Award [Line Items]              
Unrecognized pre-tax noncash compensation   $ 33,100     $ 33,100 $ 19,700  
Allocated share based compensation expense $ 3,976 1,343 $ 530 $ 1,331 $ 4,569 $ 1,900 $ 1,200
ESPP percentage         15.00%    
Expected weighted average period         3 years 3 months 18 days 2 years 6 months  
Cost Of Services              
Share Based Compensation Arrangement By Share Based Payment Award [Line Items]              
Stock based compensation expenses 200            
Allocated share based compensation expense 156 3 28 69 $ 76 $ 100 200
Selling, General and Administrative Expenses              
Share Based Compensation Arrangement By Share Based Payment Award [Line Items]              
Stock based compensation expenses 3,800            
Allocated share based compensation expense 3,820 1,285 452 1,135 4,317 1,600 900
Product And Technology Expense              
Share Based Compensation Arrangement By Share Based Payment Award [Line Items]              
Stock based compensation expenses 0            
Allocated share based compensation expense 0 $ 55 $ 50 $ 127 $ 176 $ 200 $ 100
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   11,339,126     11,339,126    
Successor Plan              
Share Based Compensation Arrangement By Share Based Payment Award [Line Items]              
Stock options plan expiration period         10 years 10 years  
Number of units, issued         0    
Predecessor Plan              
Share Based Compensation Arrangement By Share Based Payment Award [Line Items]              
Stock based compensation expenses $ 3,900            
Share-based Payment Arrangement, Option              
Share Based Compensation Arrangement By Share Based Payment Award [Line Items]              
Vesting percentage   50.00%     50.00%    
Vesting period   5 years     5 years    
Unrecognized pre-tax noncash compensation   $ 22,100     $ 22,100    
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% 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% 20.00%  
Vesting period         5 years 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 5 years  
Restricted Stock Agreements [Member]              
Share Based Compensation Arrangement By Share Based Payment Award [Line Items]              
Unrecognized pre-tax noncash compensation   10,400     $ 10,400    
Restricted Stock Units [Member]              
Share Based Compensation Arrangement By Share Based Payment Award [Line Items]              
Unrecognized pre-tax noncash compensation   $ 600     $ 600    
Class B Awards [Member]              
Share Based Compensation Arrangement By Share Based Payment Award [Line Items]              
Vesting percentage 20.00%           20.00%
Vesting period 5 years           5 years
Stock options plan expiration period 10 years           10 years
Profit interest unit, shares 1,700,051           1,700,051
Class C Awards              
Share Based Compensation Arrangement By Share Based Payment Award [Line Items]              
Vesting percentage 50.00%           50.00%
Vesting period 5 years           5 years
Stock options plan expiration period 10 years           10 years
Profit interest unit, shares 12,621,955           12,621,955
Class C Awards | Share-based Payment Arrangement, Tranche One              
Share Based Compensation Arrangement By Share Based Payment Award [Line Items]              
Vesting percentage 20.00%            
Profit Interest Units [Member]              
Share Based Compensation Arrangement By Share Based Payment Award [Line Items]              
Unrecognized pre-tax noncash compensation           $ 11,500  
Option Units [Member]              
Share Based Compensation Arrangement By Share Based Payment Award [Line Items]              
Unrecognized pre-tax noncash compensation           $ 8,200