feat: Replace JavaScript events with Web Components

[Mopsgamer]

Summary

Refactor parts of the application to use Web Components powered by Lit instead of JavaScript events and methods.

Feature Details

The current implementation relies heavily on JavaScript event listeners and imperative
DOM manipulation, leading to code complexity. Replacing these with Web Components will
enhance encapsulation, modularity, and maintainability.

Suggested migration:

• Use Lit to create custom elements for reusable UI components (e.g., chat window,
  message list, input box).
• Ensure each component handles its own state and lifecycle independently.
• Minimize direct DOM manipulation by leveraging declarative bindings in Lit.

Additional Information

Migrating incrementally is recommended. The chat window should be the first component to
transition, handling scrolling and message updates internally.