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Transactions - Allocation of Acquisition Cost (Details) - USD ($)
$ in Thousands
 5 Months Ended 9 Months Ended
Jan. 20, 2023
Aug. 01, 2022
Jun. 30, 2023
Sep. 30, 2023
Sep. 30, 2022
Dec. 31, 2022
Dec. 31, 2021
Purchase consideration:              
Cash       $ 388,246 $ 245,021    
Liabilities assumed:              
Goodwill       1,117,543 $ 722,790 $ 722,774 $ 426,297
Measurement period adjustment       $ (391)      
NIA              
Purchase consideration:              
Cash $ 387,823            
Fair value of Class A common stock issued 261,271            
Fair value of contingent consideration 66,600            
Total consideration 715,694            
Tangible assets acquired:              
Accounts receivable 28,065            
Prepaid expenses and other current assets 675            
Total tangible assets acquired 28,740            
Identifiable intangible assets acquired:              
Total identifiable intangible assets acquired 404,000            
Liabilities assumed:              
Accrued liabilities 5,409            
Accrued compensation and employee benefits 6,173            
Deferred tax liabilities, net 100,486            
Deferred revenue 142            
Total liabilities assumed 112,210            
Goodwill 395,164            
Net assets acquired 715,694            
Measurement period adjustment     $ (400)        
NIA | Customer relationships              
Identifiable intangible assets acquired:              
Total identifiable intangible assets acquired 345,100            
NIA | Technology              
Identifiable intangible assets acquired:              
Total identifiable intangible assets acquired 50,700            
NIA | Corporate trade name              
Identifiable intangible assets acquired:              
Total identifiable intangible assets acquired $ 8,200            
IPG              
Purchase consideration:              
Cash   $ 256,488          
Fair value of Class A common stock issued   130,175          
Fair value of contingent consideration   75,000          
Total consideration   461,663          
Tangible assets acquired:              
Accounts receivable   34,155          
Prepaid expenses and other current assets   636          
Other non-current assets   1,393          
Total tangible assets acquired   36,184          
Identifiable intangible assets acquired:              
Total identifiable intangible assets acquired   195,700          
Liabilities assumed:              
Accounts payable   7,997          
Accrued liabilities   8,083          
Accrued compensation and employee benefits   423          
Deferred tax liabilities, net   48,671          
Deferred revenue   321          
Operating lease liabilities   1,323          
Total liabilities assumed   66,818          
Goodwill   296,597          
Net assets acquired   461,663          
IPG | Customer relationships              
Identifiable intangible assets acquired:              
Total identifiable intangible assets acquired   154,000          
IPG | Technology              
Identifiable intangible assets acquired:              
Total identifiable intangible assets acquired   23,900          
IPG | Corporate trade name              
Identifiable intangible assets acquired:              
Total identifiable intangible assets acquired   $ 17,800