Dependency injection for FormElement #process callback
Dependency injection for any method of a class is done for the whole class. So if you have a dependency for the method you're adding for any method in the class, you will set that as a dependency for the whole class, not just a single function. However, #process callbacks are static functions, and static functions cannot use dependency injection. They should use the \Drupal::service() method, which is for static functions and procedural code.