feat: Optimize search requests with AbortController

[tony140407]

🎯 Motivation

Currently, when users type quickly in the search box, multiple API requests
are sent simultaneously. This can cause:

• Race conditions where stale responses override newer results
• Unnecessary load on the Meilisearch server
• Poor user experience with flickering results

🔧 Changes

• Add AbortController to cancel previous search requests when a new one starts
• Pass signal to the Meilisearch SDK search method (3rd parameter)
• Handle AbortError gracefully without showing error states
• Clean up ongoing requests when component unmounts
• Fix incorrect onReset() calls in error handlers that could cancel active requests

✅ Testing

Tested with:

• Network throttling (Slow 3G) to verify old requests are properly cancelled
• Rapid typing to confirm no race conditions occur
• Chrome DevTools Network tab shows "cancelled" status for aborted requests

📸 Screenshots

---

Happy to make any adjustments based on feedback! 😊

[amrbashir]

Apologoies for the late reply, I left a few comments. Could you also add a change file in .changes directory similar to this one https://github.com/tauri-apps/meilisearch-docsearch/blob/e5c670756e46f1f785b9c7a694eb337f5f4ce690/.changes/check-composition-event.md?plain=1

[tony140407]

@amrbashir Thanks for the review! I've addressed all the feedback:

• Added changelog in .changes/
• Collapsed the abort check to a single line
• Split into resetState(screenState) (pure UI reset) and onReset() (abort + reset) — kept the onReset name since it's passed as a prop to DocSearchModalSearchBox
• resetState is used in .catch() / .then() where the request already completed
• Restored the error reset for the !res case to avoid leaving the UI in a loading state

Ready for another look when you have a chance.

[amrbashir]

Thank you