[React 19][EuiFieldSearch] Console Error reported in React19 dev mode

**Describe the bug**
On a custom application that uses this library and the Renovate bot, the React version was updated. Then I started seeing errors in the Turbopack helper when the application was ran using `npm run dev`.

**Impact and severity**
The search box seems to function-ish but I did not test it extensively.

**Environment and versions**
- EUI version: 114.1.0
- React version: 19.2.4
- Kibana version (if applicable): N/A, custom app
- Browser: Island Version 1.88.23 Chromium: 146.0.7680.178 (Official Build) (arm64)
- Operating System: MacOS Tahoe 26.4

**Minimum reproducible sandbox**
https://codesandbox.io/p/sandbox/3mwtt9

**To Reproduce**
Render the page and check for console errors.

**Expected behavior**
The error does not pop-up.

**Screenshots (Optional)**

**Additional context (Optional)**

Error Type: Console Error

Error Message:
Accessing element.ref was removed in React 19. ref is now a regular prop. It will be removed from the JSX Element type in a future release.

Next.js version: 16.2.3 (Turbopack)