code: private void addInstalledExtension(DefaultInstalledExtension installedExtension, String namespace)
      {
          addCachedExtension(installedExtension);
  
          boolean isValid = installedExtension.isValid(namespace);
  
          // Register the extension in the installed extensions for the provided namespace
          addInstalledFeatureToCache(installedExtension.getId(), namespace, installedExtension, isValid);
  
          // Add virtual extensions
          for (ExtensionId feature : installedExtension.getExtensionFeatures()) {
              addInstalledFeatureToCache(feature, namespace, installedExtension, isValid);
          }
  
          if (this.updateBackwardDependencies) {
              // Recalculate backward dependencies index
              updateMissingBackwardDependencies();
          }
      }
docs: Register a newly installed extension in backward dependencies map.
  
  @param installedExtension the installed extension to register
  @param namespace the namespace