Edit Post: Fix template part reload error by preserving original post URL

[sarthaknagoshe2002]

What?

Closes #72733

This PR prevents the browser URL from syncing to the template/template part ID when entering focus mode from within the standard post editor.

Why?

When a user edits a template part from the post editor (e.g., clicking "Edit original" on a Header), the BrowserURL component previously synced the URL to reflect the template part's internal database ID (e.g., post.php?post=321). If the user hard-reloads the page at this point, the PHP backend crashes with a "You do not have permission" error because post.php is strictly designed for standard post types, not wp_template_part.

As suggested in the issue, the most acceptable and robust fallback is to simply ensure the user is returned to the post they were originally editing upon reload.

How?

Updated the BrowserURL component within the edit-post package to detect when the editor shifts into a template or template part context. When isTemplate is true, the URL synchronization hook returns early, effectively freezing the URL on the parent post (e.g., post.php?post=636).

If a user reloads the page, they are safely dropped back into the parent post editor. If they click "Back" in the UI, the editor restores seamlessly.

Testing Instructions

1. Open a standard Post or Page in the editor.
2. Ensure template preview mode is active, double-click a template part (like the Header), and select "Edit" to enter focus mode.
3. Observe the URL in your browser. Verify that it does not change to a new ID, but remains anchored to your original post.
4. Hard refresh the page.
5. Verify that the editor loads safely back into the original post without throwing a permission error.

Screenshots or screencast

Screen.Recording.2026-07-01.at.6.24.22.PM.mov

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Co-authored-by: sarthaknagoshe2002 <sarthaknagoshe2002@git.wordpress.org>
Co-authored-by: andrewserong <andrewserong@git.wordpress.org>

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