Converted GuessInput to a StatefulWidget in Stateful widgets tutorial

[MuthuGCodes]

Rebuilding GamePage (after converting it to StatefulWidget) recreates GuessInput (which is currently a StatelessWidget), resetting its internal FocusNode and TextEditingController and breaking focus behavior. The fix is to convert GuessInput to a StatefulWidget in the "Stateful widgets" tutorial step and the example code.

Fixes #13392

[flutter-website-bot]

Staged preview of the updated docs.flutter.dev site (updated for commit 8150ada):

https://flutter-docs-prod--docs-pr13653-mg-guessinput-issue-3th19sc7.web.app

[flutter-website-bot]

Staged preview of the updated flutter.dev site (updated for commit 8150ada):

https://flutter-dev-230821--www-pr13653-mg-guessinput-issue-hk3zmet1.web.app

[lamek]

A few things to fix.

[lamek]

This file is local to your IDE. You can remove it.

[lamek]

For code excerpts in the tutorial we follow these steps:

1. Write the updated code into the corresponding /examples/FWE/lib file.
2. Add a tag like the following: <?code-excerpt "fwe/birdle/lib/step5_main.dart (GuessInput)"?>
3. Run the following command: dart run dash_site --site=docs refresh-excerpts

Following this flow will ensure the code snippets in our .MD files are always up to date with what is in the /examples dir.

[MuthuGCodes]

Incorporated review comments

[gemini-code-assist]

Code Review

This pull request converts the GuessInput widget from a StatelessWidget to a StatefulWidget in the Birdle example to properly manage the lifecycles of TextEditingController and FocusNode, including their disposal. It also updates the tutorial documentation to explain this transition. Feedback was provided to correct a conceptual explanation in the documentation regarding Flutter's widget recreation lifecycle, clarifying that controllers persist because they are moved to the persistent State object rather than being recreated with the widget instance.

[gemini-code-assist]

The explanation states that a new GuessInput instance is created on every rebuild because it was a StatelessWidget. However, in Flutter, widget instances are immutable and are recreated on almost every rebuild regardless of whether they are stateful or stateless.

The actual issue is that the TextEditingController and FocusNode were declared as fields of the GuessInput widget class itself. Because the widget is recreated on every parent rebuild, these controllers were also re-instantiated, causing the loss of focus/state and memory leaks.

By converting to a StatefulWidget, these controllers are moved to the persistent State object (_GuessInputState), which survives widget recreation.

Consider clarifying this distinction to help learners better understand Flutter's widget vs. state lifecycle.

Suggested change

	Because `GuessInput` was originally created as a `StatelessWidget`,
	every rebuild creates a new `GuessInput` instance,
	along with a new `TextEditingController` and `FocusNode`.
	This causes the text input field to lose focus after submitting a guess
	and leaves unused controllers without proper disposal.
	Because `GuessInput` was originally created as a `StatelessWidget`,
	its `TextEditingController` and `FocusNode` were stored directly in the widget class.
	Since a new widget instance is created on every rebuild, these controllers
	were recreated each time, causing the text input field to lose focus
	and leaving unused controllers without proper disposal.