$ composer why-not drupal/core ^10
drupal/core-recommended 9.5.11       requires         drupal/core (9.5.11)                                    
drupal/insert           2.0.0        requires         drupal/core (^8 || ^9)                                  
drupal/core             10.2.0-beta1 requires         symfony/console (^6.4)                                  
drupal/legacy-project   -            does not require symfony/console (but v4.4.49 is installed)              
drupal/core             10.2.0-beta1 requires         symfony/dependency-injection (^6.4)                     
drupal/legacy-project   -            does not require symfony/dependency-injection (but v4.4.49 is installed) 
drupal/core             10.2.0-beta1 requires         symfony/event-dispatcher (^6.4)                         
drupal/legacy-project   -            does not require symfony/event-dispatcher (but v4.4.44 is installed)     
drupal/core             10.2.0-beta1 requires         symfony/finder (^6.4)                                   
drupal/legacy-project   -            does not require symfony/finder (but v4.4.44 is installed)               
drupal/core             10.2.0-beta1 requires         symfony/http-foundation (^6.4)                          
drupal/legacy-project   -            does not require symfony/http-foundation (but v4.4.49 is installed)      
drupal/core             10.2.0-beta1 requires         symfony/http-kernel (^6.4)                              
drupal/legacy-project   -            does not require symfony/http-kernel (but v4.4.51 is installed)          
drupal/core             10.2.0-beta1 requires         symfony/mime (^6.4)                                     
drupal/legacy-project   -            does not require symfony/mime (but v5.4.13 is installed)                 
drupal/core             10.2.0-beta1 requires         symfony/routing (^6.4)                                  
drupal/legacy-project   -            does not require symfony/routing (but v4.4.44 is installed)              
drupal/core             10.2.0-beta1 requires         symfony/serializer (^6.4)                               
drupal/legacy-project   -            does not require symfony/serializer (but v4.4.47 is installed)           
drupal/core             10.2.0-beta1 requires         symfony/validator (^6.4)                                
drupal/legacy-project   -            does not require symfony/validator (but v4.4.48 is installed)            
drupal/core             10.2.0-beta1 requires         symfony/process (^6.4)                                  
drupal/legacy-project   -            does not require symfony/process (but v4.4.44 is installed)              
drupal/core             10.2.0-beta1 requires         symfony/yaml (^6.4)                                     
drupal/legacy-project   -            does not require symfony/yaml (but v4.4.45 is installed)                 
drupal/core             10.2.0-beta1 requires         twig/twig (^3.5.0)                                      
drupal/legacy-project   -            does not require twig/twig (but v2.15.5 is installed)                    
drupal/core             10.2.0-beta1 requires         doctrine/annotations (^1.14)                            
drupal/legacy-project   -            does not require doctrine/annotations (but 1.13.3 is installed)          
drupal/core             10.2.0-beta1 requires         guzzlehttp/guzzle (^7.5)                                
drupal/legacy-project   -            does not require guzzlehttp/guzzle (but 6.5.8 is installed)              
drupal/core             10.2.0-beta1 requires         guzzlehttp/psr7 (^2.4.5)                                
drupal/legacy-project   -            does not require guzzlehttp/psr7 (but 1.9.1 is installed)                
drupal/core             10.2.0-beta1 requires         asm89/stack-cors (^2.1)                                 
drupal/legacy-project   -            does not require asm89/stack-cors (but 1.3.0 is installed)               
drupal/core             10.2.0-beta1 requires         psr/log (^3.0)                                          
drupal/legacy-project   -            does not require psr/log (but 1.1.4 is installed)                        
Not finding what you were looking for? Try calling `composer update "drupal/core:^10" --dry-run` to get another view on the problem.

これをみると、coreの要件があってないというのが、たくさんあるけど、

symfony/console (^6.4)             
symfony/dependency-injection (^6.4)
symfony/event-dispatcher (^6.4)                         
symfony/finder (^6.4)
symfony/http-foundation (^6.4)                          
symfony/http-kernel (^6.4)
symfony/mime (^6.4)                                     
symfony/routing (^6.4)                                  
symfony/serializer (^6.4)                               
symfony/validator (^6.4)                                
symfony/process (^6.4)                                  
symfony/yaml (^6.4)                                     
twig/twig (^3.5.0)                                      
doctrine/annotations (^1.14)                            
guzzlehttp/guzzle (^7.5)                                
guzzlehttp/psr7 (^2.4.5)                                
asm89/stack-cors (^2.1)                                 
psr/log (^3.0)                                          

これらは全部coreの中身だから、使用者がどうこうできる内容じゃないよね。となると、うえからの2行目のinsertだけさじょすればいけるのでは？とおもってしまうが、どうでしょうか。