When a user tries to reorder a page tree alphabetically and doesn't have the proper permissions in one or more child pages to do so (that means, there is an "Edit page" restriction somewhere in the child pages), the UI will reorder the page tree within the "Reorder pages" tab and won't show any type of error or warning message. HAR file will show that server returned a "403 Forbidden" error. When the user refreshes the page or goes to the Space main page, page tree remains with the original order.

The suggestion would be to add some error or warning message in this specific scenario.