For #26329 Refactor the search widget to use the A-C common behaviour

[iorgamgabriel]

It should behave like the current version .

Pull Request checklist

• [ ] Tests: This PR includes thorough tests or an explanation of why it does not
• [ ] Screenshots: This PR includes screenshots or GIFs of the changes made or an explanation of why it does not
• [ ] Accessibility: The code in this PR follows accessibility best practices or does not include any user facing features. In addition, it includes a screenshot of a successful accessibility scan to ensure no new defects are added to the product.

QA

• [x] QA Needed

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GitHub Automation

Fixes #26329