[Reader IA][Search] Hook Search top bar action to existing functionality

[thomashorta]

Fixes #19923

The search action in the new Reader top bar was not working so far, so this PR hooks it to the existing logic to show/hide it when the search feature is supported (logged into WPcom account or not) and to open the existing Search screen when tapped.

---

To Test:

Search action visibility

The search action should only show up for users logged into Jetpack with a WPcom account, so it's hidden for users logged with self-hosted sites.

19923-reader-ia-search-hidden-self-hosted.mp4

Hidden

1. Log into Jetpack with a self-hosted site
2. Go to Reader
3. Verify the search action icon is not shown in the top bar for any feeds

Showing

1. Log into Jetpack with a WPcom account
2. Go to Reader
3. Verify the search action icon is shown in the top bar for all feeds

Search action opening Search screen

Tapping the search action should redirect the user to the existing Reader Search feature.

19923-reader-ia-search-action.mp4

1. Log into Jetpack with a WPcom account
2. Go to Reader
3. Tap the search action icon in the top bar
4. Verify it opens the existing Search screen

---

Regression Notes

1. Potential unintended areas of impact

   • N/A

2. What I did to test those areas of impact (or what existing automated tests I relied on)

   • N/A

3. What automated tests I added (or what prevented me from doing so)

   • None yet (unit tests for the top bar will be done in a different PR)

---

PR Submission Checklist:

• I have completed the Regression Notes.
• I have considered adding accessibility improvements for my changes.
• I have considered if this change warrants user-facing release notes and have added them to RELEASE-NOTES.txt if necessary.

---

UI Changes Testing Checklist:

N/A

• Portrait and landscape orientations.
• Light and dark modes.
• Fonts: Larger, smaller and bold text.
• High contrast.
• Talkback.
• Languages with large words or with letters/accents not frequently used in English.
• Right-to-left languages. (Even if translation isn’t complete, formatting should still respect the right-to-left layout)
• Large and small screen sizes. (Tablet and smaller phones)
• Multi-tasking: Split screen and Pop-up view. (Android 10 or higher)

[peril-wordpress-mobile]

	Warnings
⚠️	PR is not assigned to a milestone.

Generated by 🚫 dangerJS

[dangermattic]

	1 Warning
⚠️	PR is not assigned to a milestone.

Generated by 🚫 Danger

[wpmobilebot]

📲 You can test the changes from this Pull Request in Jetpack by scanning the QR code below to install the corresponding build.

	App Name	Jetpack
	Flavor	Jalapeno
	Build Type	Debug
	Version	pr19927-300b246
	Commit	300b246
	Direct Download	jetpack-prototype-build-pr19927-300b246.apk

Note: Google Login is not supported on these builds.

[wpmobilebot]

📲 You can test the changes from this Pull Request in WordPress by scanning the QR code below to install the corresponding build.

	App Name	WordPress
	Flavor	Jalapeno
	Build Type	Debug
	Version	pr19927-300b246
	Commit	300b246
	Direct Download	wordpress-prototype-build-pr19927-300b246.apk

Note: Google Login is not supported on these builds.

[RenanLukas]

Thanks for the PR, @thomashorta

It's working as expected and code LGTM