feat(examples): update client_app and postly implementation details

- Refactored and updated pages, router, DI modules, and feature implementations in both example projects:
  - client_app: main.dart and my_home_page.dart updated for improved navigation and structure.
  - postly: updated DI wiring, presentation pages, repository implementation, and routing logic.
- Applied small improvements and code consistency changes in the examples.

docs: add new documentation assets and benchmarking script

BREAKING CHANGE:
Examples now reflect the latest changes in the DI framework and are ready for Dart 3.8+ and cherrypick_generator element2 API compatibility.

examples/postly/lib/data/post_repository_impl.dart

@@ -12,9 +12,9 @@ class PostRepositoryImpl implements PostRepository {
   Future<Either<Exception, List<Post>>> getPosts() async {
     try {
       final posts = await api.getPosts();
-      return Right(posts
-          .map((e) => Post(id: e.id, title: e.title, body: e.body))
-          .toList());
+      return Right(
+        posts.map((e) => Post(id: e.id, title: e.title, body: e.body)).toList(),
+      );
     } catch (e) {
       return Left(Exception(e.toString()));
     }