docs: refactor AutoCompleteInput example to remove unnecessary useRef

[mlnwns]

Overview

This PR introduces an improvement to the AutoCompleteInput example in the documentation (without-react-simplikit.tsx).

The debouncing logic has been refactored to remove the unnecessary useRef (searchTimeoutRef) and the redundant clearTimeout defensive code. By assigning the timer to a local timeoutId variable and leveraging closures for the cleanup function, the code becomes much more declarative and concise.

Additionally, this change cleanly resolves the NodeJS.Timeout type dependency issue between browser and Node environments, enhancing type safety and the developer experience without changing the component's external behavior.

Checklist

• Did you write the test code?
• Have you run yarn run fix to format and lint the code and docs?
• Have you run yarn run test:coverage to make sure there is no uncovered line?
• Did you write the JSDoc?

[Copilot]

Pull request overview

This PR refactors the AutoCompleteInput example in the documentation to demonstrate a cleaner approach to debouncing. The changes remove the unnecessary useRef hook and defensive clearTimeout checks by leveraging closures and React's built-in cleanup mechanism.

Changes:

• Removed searchTimeoutRef useRef hook from the "without-react-simplikit" example
• Refactored debouncing logic to use a local timeoutId variable with closure-based cleanup
• Simplified cleanup function from a defensive null-check pattern to a single line

Reviewed changes

Copilot reviewed 2 out of 2 changed files in this pull request and generated no comments.

File	Description
docs/core/why-react-simplikit-matters.md	Updated English documentation example to demonstrate cleaner timeout cleanup pattern
docs/ko/core/why-react-simplikit-matters.md	Updated Korean documentation example with identical refactoring as English version

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[kimyouknow]

thanks!