Migrate search upsell page to unified AdminHeader

[CGastrell]

Part of JETPACK-1355

Summary

• Migrates the search upsell page from the deprecated header prop to the new title/subTitle/actions props on AdminPage
• Moves the license activation link from the custom Header component into the actions prop
• Removes the wrapping <div> around AdminPage
• Updates dashboard-page.scss to scope padding reset with :not(:has(.uses-new-admin-ui))

Depends on #47313.

Before	After

Then there's this screen which seems unreachable (old pricing 2022-08), and it's completely broken. We should remove it entirely:

Does this pull request change what data or activity we track or use?

No. Presentational change only.

Testing instructions:

• jetpack build packages/search passes
• jetpack test js packages/search passes
• Visual check: search upsell page renders header with Jetpack bolt icon + "Search" title + subtitle

🤖 Generated with Claude Code

[github-actions]

Are you an Automattician? Please test your changes on all WordPress.com environments to help mitigate accidental explosions.

• To test on WoA, go to the Plugins menu on a WoA dev site. Click on the "Upload" button and follow the upgrade flow to be able to upload, install, and activate the Jetpack Beta plugin. Once the plugin is active, go to Jetpack > Jetpack Beta, select your plugin (Jetpack), and enable the update/normalize-search-admin-header branch.
• To test on Simple, run the following command on your sandbox:

bin/jetpack-downloader test jetpack update/normalize-search-admin-header

Interested in more tips and information?

• In your local development environment, use the jetpack rsync command to sync your changes to a WoA dev blog.
• Read more about our development workflow here: PCYsg-eg0-p2
• Figure out when your changes will be shipped to customers here: PCYsg-eg5-p2

[github-actions]

Thank you for your PR!

When contributing to Jetpack, we have a few suggestions that can help us test and review your patch:

• ✅ Include a description of your PR changes.
  
• ✅ Add a "[Status]" label (In Progress, Needs Review, ...).
  
• ✅ Add testing instructions.
  
• ✅ Specify whether this PR includes any changes to data or privacy.
  
• ✅ Add changelog entries to affected projects
  

This comment will be updated as you work on your PR and make changes. If you think that some of those checks are not needed for your PR, please explain why you think so. Thanks for cooperation 🤖

---

Follow this PR Review Process:

1. Ensure all required checks appearing at the bottom of this PR are passing.
2. Make sure to test your changes on all platforms that it applies to. You're responsible for the quality of the code you ship.
3. You can use GitHub's Reviewers functionality to request a review.
4. When it's reviewed and merged, you will be pinged in Slack to deploy the changes to WordPress.com simple once the build is done.

If you have questions about anything, reach out in #jetpack-developers for guidance!

[jp-launch-control]

Code Coverage Summary

No summary data is available for parent commit 2985c11, so cannot calculate coverage changes. 😴

If that commit is a feature branch rather than a trunk commit, this is expected. Otherwise, this should be updated once coverage for 2985c11 is available.

Full summary · PHP report · JS report

_{Coverage check overridden by Coverage tests to be added later Use to ignore the Code coverage requirement check when tests will be added in a follow-up PR .}