Classic header uses the new search button and action buttons

## Summary

PR 287570 aligns the Classic solution view header with the Chrome Next header: the global search field becomes the same search button used in solution views (a compact icon, or an expanded button with the placeholder Find apps, content, and more.), and the right-side buttons use the same components as solution views. The Ctrl+/ and Command+/ shortcut still opens the search. PR 288395 then removes the unused classic chrome APIs and the legacy header pieces they powered, including the What's new newsfeed button in the classic header (news remain available from the help menu and the sidebar) and the old search bar strings. Nothing changes for solution-view spaces or serverless projects.

**Why this needs docs:** The published Find apps and objects page still holds (search field in the global header, same keyboard shortcut) and no doc describes the classic header newsfeed button, so the only exposure is a possibly outdated screenshot of the classic search field. Confidence stays under 0.8 because the evidence for the visual change is screenshot-based.

## Resources

- PR [#288395](https://github.com/elastic/kibana/pull/288395) — [Chrome] Clean up leftover classic Chrome APIs
- PR [#287570](https://github.com/elastic/kibana/pull/287570) — [Chrome] Classic header consumes chrome.next registrations

Screenshots from PR


## Availability

| Channel | Details |
|---------|---------|
| **Stack** | v9.6.0 |
| **Serverless** | N/A |
| **Feature flag** | None — active by default |

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## If you chose to document this

[Find apps and objects](https://www.elastic.co/docs/explore-analyze/find-and-organize/find-apps-and-objects) > Introduction
- **What the docs say:** To quickly find apps and the objects you create, use the search field in the global header. ... Use the keyboard shortcut to open the search field at any time: Ctrl+/ on Windows and Linux, or Command+/ on macOS.
- **What to add:** The wording stays valid. Check the Example of searching for apps screenshot: in Classic view the header now shows the same search button as solution views instead of the old inline search field, so a Classic-view screenshot from before 9.6 no longer matches. If the screenshot needs replacing, flag it rather than replacing it yourself. Stack only, from 9.6.0 (Classic view does not exist in serverless).