Dart 3: How to generate builder files into a custom folder instead of been next to the original class

Question

How can I change the location where the files are going to be generated from this command dart run build_runner build.

Current folder project structure after running that command:

├── lib
│   ├── entity_generator.dart
│   └── test_files
│       ├── annotation
│       │   └── annotation.dart
│       ├── classes2.dart
│       ├── classes2.entity.dart
│       ├── classes.dart
│       ├── classes.entity.dart
│       └── gen
├── pubspec.lock
└── pubspec.yaml

Current folder project structure after generating them into the custom folder:

├── lib
│   ├── entity_generator.dart
│   └── test_files
│       ├── annotation
│       │   └── annotation.dart
│       ├── classes2.dart
│       ├── classes.dart
│       └── gen
│           ├── classes.entity.dart
|           └── classes2.entity.dart
├── pubspec.lock
└── pubspec.yaml

entity_generator.dart:

class EntityGenerator extends GeneratorForAnnotation<Entity> {
  @override
  generateForAnnotatedElement(Element element, ConstantReader annotation, BuildStep buildStep) {
    if (element is! ClassElement) {
      throw InvalidGenerationSourceError('`@Entity` can only be used on classes.', element: element);
    }

    final className = element.displayName;
    final buffer = StringBuffer();

    // Generate the class with entity exports
    buffer.writeln('class $className extends Entity {}');
    return buffer.toString();
  }
}

Builder entityBuilder(BuilderOptions options) => LibraryBuilder(EntityGenerator(), generatedExtension: '.entity.dart');

build.yaml:

targets:
  $default:
    builders:
      test_app|export_locating_builder:
        enabled: true

builders:
  export_locating_builder:
    import: "package:test_app/entity_generator.dart"
    builder_factories: [ "entityBuilder" ]
    build_extensions: {
      '^lib/test_files/{{}}.dart': ['lib/test_files/gen/{{}}.entity.dart']
    }
    auto_apply: dependents
    build_to: source

For the moment even if I did the part {{}} the files will still be generated next to the original class instead of the gen folder. Can anyone explain to me what exactly I am doing wrong here?