Require three characters before searching docs

[enriquegh]

Summary

• Wait until the trimmed query contains at least three characters before requesting Algolia results.
• Show a minimum-length prompt for short input and hide previous results when deleting below the threshold.
• Preserve curated suggestions before typing.

Verification

• pnpm exec tsc --noEmit passed.
• Targeted ESLint and git diff --check passed.
• Browser checks: one- and two-character queries send no search requests; api returns results; deleting back to two characters hides results; whitespace and product filters cannot bypass the minimum; clearing restores curated suggestions.
• Inspected the rendered short-query state.

Amp thread: https://ampcode.com/threads/T-01a0ca8a-763a-7208-8639-edbaaa47c876

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Project	Deployment	Actions	Updated
sourcegraph-docs	Ready	Preview	Sep 22, 2026 8:02pm UTC

[github-actions]

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[marcleblanc2]

We'll need to remember to revisit this with the migration