Administration: Refresh stale post list tables

[Sukhendu2002]

What this PR does

Fixes stale post list-table rows when a post is changed in another browser window or after restoring the list through browser history.

Trac ticket: https://core.trac.wordpress.org/ticket/65461

Manual testing

Use two browser windows logged into the same WordPress installation.

External post update

1. In window A, open Posts → All Posts and note a post title.
2. In window B, edit that post, change its title, and save.
3. Return to window A and wait up to 10 seconds for Heartbeat.
4. Confirm that the list reloads and displays the updated title.

Quick Edit preservation

1. In window A, open Quick Edit for a post.
2. Change the title but do not click Update.
3. In window B, edit and save the same post.
4. Return to window A and trigger Heartbeat or wait up to 10 seconds.
5. Confirm that the page does not reload and the unsaved Quick Edit title remains.
6. Click Cancel in Quick Edit.
7. Trigger Heartbeat again.
8. Confirm that the list reloads and displays the title saved in window B.

Filter membership

1. Create a draft post.
2. In window A, open Posts → All Posts and select the Published filter.
3. In window B, publish the draft.
4. Return to window A and trigger Heartbeat.
5. Confirm that the list reloads and the newly published post appears.

Creation and deletion

1. Keep Posts → All Posts open in window A.
2. Create and publish a post in window B.
3. Trigger Heartbeat in window A and confirm that the new post appears.
4. Trash the post in window B.
5. Trigger Heartbeat again and confirm that the row disappears.

Use of AI Tools

AI assistance: Yes
Tool(s): pi coding agent
Model(s): GPT-5.6
Used for: Initial code skeleton, code review, test suggestion and PR description drafting; final implementation and tests were reviewed and edited by me.

This Pull Request is for code review only. Please keep all other discussion in the Trac ticket. Do not merge this Pull Request. See GitHub Pull Requests for Code Review in the Core Handbook for more details.

[github-actions]

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Test this pull request with WordPress Playground.

[github-actions]

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