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Merger and reverse recapitalization - Narrative (Details)
$ / shares in Units, $ in Millions
 12 Months Ended
Mar. 30, 2023
USD ($)
$ / shares
shares
Dec. 31, 2024
$ / shares
shares
Dec. 31, 2023
shares
Dec. 11, 2024
$ / shares
Dec. 31, 2022
shares
Schedule Of Reverse Recapitalization [Line Items]          
Shares issued (in shares) 47,594,936        
Options outstanding (in shares)   5,031,303 3,886,248   870,567
Options exercisable, exercise price (in dollars per share) | $ / shares   $ 8.67      
Purchase price per share (in dollars per share) | $ / shares       $ 4.41  
Exchange ratio of business combination     373.47    
Gross proceeds | $ $ 128.6        
Cash from PIPE Financing | $ 4.7        
Transaction costs | $ $ 25.7        
Legacy UHG          
Schedule Of Reverse Recapitalization [Line Items]          
Outstanding options assumed (in shares) 2,403        
Options issued upon exchange (in shares) 897,585        
Outstanding warrants assumed (in shares) 5,000        
DHHC Class B Common Stock          
Schedule Of Reverse Recapitalization [Line Items]          
Earnout shares remaining after those surrendered (in shares) 6,738,621        
Shares forfeited (in shares) 2,577,697        
Note Purchase Agreement          
Schedule Of Reverse Recapitalization [Line Items]          
Payments of debt issuance costs | $ $ 3.5        
Note Purchase Agreement | Convertible Debt          
Schedule Of Reverse Recapitalization [Line Items]          
Original principal amount | $ $ 80.0        
Related Party | DHHC Class B Common Stock          
Schedule Of Reverse Recapitalization [Line Items]          
Shares surrendered (in shares) 1,886,379        
DHHC sponsor shareholders – UHG Class A Common Shares | Related Party          
Schedule Of Reverse Recapitalization [Line Items]          
Shares issued (in shares) 4,160,924        
Convertible Note Investors – UHG Class A Common Shares | Related Party          
Schedule Of Reverse Recapitalization [Line Items]          
Shares issued (in shares) 744,588        
Diamondhead Holdings Corp. ("DHHC")          
Schedule Of Reverse Recapitalization [Line Items]          
Exchange ratio of business combination 373.47        
Gross proceeds | $ $ 43.9        
Debt issuance costs | $ 5.0        
Net cash proceeds | $ 71.5        
Transaction costs | $ 13.6        
Legacy UHG          
Schedule Of Reverse Recapitalization [Line Items]          
Transaction costs | $ $ 12.1        
Assumed Warrants          
Schedule Of Reverse Recapitalization [Line Items]          
Exercise price (in dollars per share) | $ / shares $ 4.05        
Outstanding warrants (in shares) 1,867,368        
Assumed Warrants | Legacy UHG          
Schedule Of Reverse Recapitalization [Line Items]          
Shares called by warrants (in shares) 1,867,368        
Warrants Issued in Connection with the Dhhc Initial Public Offering          
Schedule Of Reverse Recapitalization [Line Items]          
Exercise price (in dollars per share) | $ / shares $ 11.50        
GSH Class A Common Shares | Legacy UHG          
Schedule Of Reverse Recapitalization [Line Items]          
Issued and outstanding shares exchanged (in shares) 1,000        
Class A          
Schedule Of Reverse Recapitalization [Line Items]          
Shares issued (in shares) 1,755,061        
Common stock, outstanding (in shares) 10,621,060 21,607,007 11,382,282    
Options outstanding (in shares) 897,585        
Options exercisable, exercise price (in dollars per share) | $ / shares $ 2.81        
Earnout shares reversed (in shares) 21,886,379        
Earnout shares to be awarded to certain particular holders (in shares) 20,000,000 20,000,000      
Class A | Legacy UHG          
Schedule Of Reverse Recapitalization [Line Items]          
Shares issued upon exchange (in shares) 373,471        
Class A | Note Purchase Agreement | Convertible Debt          
Schedule Of Reverse Recapitalization [Line Items]          
Shares issued (in shares) 744,588        
Class A | Share Lock-Up Agreements          
Schedule Of Reverse Recapitalization [Line Items]          
Purchase price per share (in dollars per share) | $ / shares $ 0.01        
Shares agreed to issue to each investor (in shares) 0.25        
Shares agreed to issue (up to) (in shares)   421,099      
Class A | Related Party | DHHC Class B Common Stock          
Schedule Of Reverse Recapitalization [Line Items]          
Earnout shares reversed (in shares) 1,886,379        
Class A | Assumed Warrants          
Schedule Of Reverse Recapitalization [Line Items]          
Shares called by warrants (in shares) 1,867,368        
GSH Class B Common Shares | Legacy UHG          
Schedule Of Reverse Recapitalization [Line Items]          
Issued and outstanding shares exchanged (in shares) 99,000        
Class B          
Schedule Of Reverse Recapitalization [Line Items]          
Common stock, outstanding (in shares) 36,973,876 36,973,876 36,973,876    
Class B | Legacy UHG          
Schedule Of Reverse Recapitalization [Line Items]          
Shares issued upon exchange (in shares) 36,973,876        
Common Class First | PIPE Subscription Agreements          
Schedule Of Reverse Recapitalization [Line Items]          
Shares issued (in shares) 471,500        
Common Class First | PIPE Subscription Agreements | Convertible Debt          
Schedule Of Reverse Recapitalization [Line Items]          
Purchase price per share (in dollars per share) | $ / shares $ 10.00        
Common Class Second | PIPE Subscription Agreements          
Schedule Of Reverse Recapitalization [Line Items]          
Shares issued (in shares) 117,874        
Purchase price per share (in dollars per share) | $ / shares $ 0.01