Task: Create Example for Deeply Nested Components

Summary

Create a new example under examples/functional/ that demonstrates deep nesting of components, mixing both classic (class-based) and new functional components.

Rationale

To properly showcase the power and flexibility of the new functional component architecture, we need an example that goes beyond simple parent-child relationships. This example should illustrate:

1. A functional component hosting multiple child components.
2. A functional component hosting a classic component, which in turn hosts another functional component.
3. A classic component hosting a functional component.
4. State being passed down through multiple levels of nesting.
5. The reactive updates (component.set()) working correctly through the entire hierarchy.

This will serve as a clear, practical guide for developers on how to structure complex UIs and manage component composition effectively.

Acceptance Criteria

• A new folder is created under examples/functional/.
• The example contains at least three levels of component nesting.
• The nesting hierarchy includes a mix of functional and classic components.
• The top-level component's state drives changes in the deeply nested children.
• The example is clean, well-documented, and easy to understand.