Fix a few issues in the Parent Page picker

[crazytonyli]

Description

Fixes a few issues in the parent page picker:

• The picker should not show the current page.
• The picker should not show a hierarchical view.
• Add deboucne to the search input field.
• The top-level page may incorrectly show a "Parent Page: (ID: 0)".

[dangermattic]

	1 Warning
⚠️	View files have been modified, but no screenshot or video is included in the pull request. Consider adding some for clarity.

Generated by 🚫 Danger

[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
	Configuration	Release-Alpha
	Build Number	31644
	Version	PR #25414
	Bundle ID	org.wordpress.alpha
	Commit	3cb1eb7
	Installation URL	3dhkk9t9inon0

Automatticians: You can use our internal self-serve MC tool to give yourself access to those builds if needed.

[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
	Configuration	Release-Alpha
	Build Number	31644
	Version	PR #25414
	Bundle ID	com.jetpack.alpha
	Commit	3cb1eb7
	Installation URL	70pd0j0j6tbp8

Automatticians: You can use our internal self-serve MC tool to give yourself access to those builds if needed.

[sonarqubecloud]

Quality Gate passed

Issues
0 New issues
0 Accepted issues

Measures
0 Security Hotspots
0.0% Coverage on New Code
0.0% Duplication on New Code

See analysis details on SonarQube Cloud

[wpmobilebot]

Version 26.8 has now entered code-freeze, so the milestone of this PR has been updated to 26.9.