What’s the _wp_desired_post_slug value for?

See this line in WordPress core.

Explanation: When you move a post to the trash, _wp_desired_post_slug holds the slug that was desired for that post (now in the trash); i.e., when you move a post to the trash, WordPress suffixes the old slug so that it becomes available again, but it remembers the slug that you desired, just in case you decide to move it out of the trash and restore it.