Sites: Update the empty state for search results

[arthur791004]

Part of DOTMSD-1068

Proposed Changes

• Update the EmptyState when there are no values return from the search.
• TODO: Confirm the actions

Why are these changes being made?

• Improve the experience of the empty state

Testing Instructions

• Go to /sites
• Search any keyword until there is no result
• Ensure the empty search state is correct

Pre-merge Checklist

• Has the general commit checklist been followed? (PCYsg-hS-p2)
• Have you written new tests for your changes?
• Have you tested the feature in Simple (P9HQHe-k8-p2), Atomic (P9HQHe-jW-p2), and self-hosted Jetpack sites (PCYsg-g6b-p2)?
• Have you checked for TypeScript, React or other console errors?
• Have you tested accessibility for your changes? Ensure the feature remains usable with various user agents (e.g., browsers), interfaces (e.g., keyboard navigation), and assistive technologies (e.g., screen readers) (PCYsg-S3g-p2).
• Have you used memoizing on expensive computations? More info in Memoizing with create-selector and Using memoizing selectors and Our Approach to Data
• Have we added the "[Status] String Freeze" label as soon as any new strings were ready for translation (p4TIVU-5Jq-p2)?
  • For UI changes, have we tested the change in various languages (for example, ES, PT, FR, or DE)? The length of text and words vary significantly between languages.
• For changes affecting Jetpack: Have we added the "[Status] Needs Privacy Updates" label if this pull request changes what data or activity we track or use (p4TIVU-aUh-p2)?

[github-actions]

Calypso Live (direct link)

https://calypso.live?image=registry.a8c.com/calypso/app:build-167995

Jetpack Cloud live (direct link)

https://calypso.live?image=registry.a8c.com/calypso/app:build-167995&env=jetpack

Automattic for Agencies live (direct link)

https://calypso.live?image=registry.a8c.com/calypso/app:build-167995&env=a8c-for-agencies

Dashboard live (direct link)

https://calypso.live?image=registry.a8c.com/calypso/app:build-167995&env=dashboard

[claude]

The description "Try again, or start a new site with the options below." seems a bit redundant since the user can see the options. Consider simplifying to just "Try a different search, or start a new site with the options below." to make it clearer what action they should take.

[matticbot]

This PR modifies the release build for the following Calypso Apps:

For info about this notification, see here: PCYsg-OT6-p2

• help-center
• notifications
• wpcom-block-editor

To test WordPress.com changes, run install-plugin.sh $pluginSlug feat/sites-empty-search-state on your sandbox.

[arthur791004]

Another approach - #108439

[arthur791004]

Closing it in favor of #108439.