Please note this message at the bottom of that support article: The sort order in the Library window is for viewing purposes only, and will not be reflected in the Bookmarks sidebar, menu or button.

The first two items on that support page - - "Sort by Name" and rearranging manually where the user is working with the right and left panes of that window - - should work fine; but the 3rd - using the Menu Bar > Views menu is a temporary sort that only holds for as long as the Library window remains opened. As soon as the Library window is closed the "sort order" in Views that you selected gets reset to the order that you have selected the next time the Library is opened. The "default" for Views is unsorted.

When I click "Show All Bookmarks", the bookmarks are listed in the NEW manually-arranged sequence).

But, when I click on "Bookmarks", the bookmarks shown under "Recently Bookmarked" are listed in a different sequence.

"Recently Bookmarked" is a so called smart folder that shows the result of a query and its content is always sorted by last date create at the top (top to bottom: newest to older bookmarks). "Recently Bookmarked" contains bookmarks that are stored in all bookmarks folders.

How do I rearrange all of my bookmarks so they stay in the order I want?

You can't use the "Recently Bookmarked" smart folder if you want to see bookmarks in a specific order because this is an automatically created list and not a real existing folder and you can't change the order of this list (sorted by date created descending).

If you sort the bookmarks via "Sort By Name" in the right-click context menu (Library or sidebar) or organize the bookmarks manually by dragging them in the desired order then this sorting is permanent.

The Library menu lists the bookmarks in the desired order.

Can I delete (or eliminate) the "Recently Bookmarked" list so I can view the Library list and click on the bookmark I want to open?