Google has updated the site move related search documentation this week. It seems like most of the changes were mostly about simplifying things around site moves, removing some content, clarification and so forth.
Gary Illyes said on Mastodon, "just cleaned it up; it collected a lot of potentially unnecessary sentences over the years. And we linked out to a couple external resources from those with more working knowledge on site moves."
I did not go through all the documentation change, but the most obvious ones I caught include these:
(1) Removed the "what is a site move" document, adding "changing hosting." and misc changes, see this sidebar navigation change to what is live versus the Wayback machine:
(2) The site move - move URL change related documents was renamed to the changing your hosting but the URL is the same and much of the content is the same. Like I said above, a lot of rewording, simplifying, removing of content.
You should go through these new docs from scratch and read them, whenever you are about to do a new site move.
In fact, yesterday, Google released a Search Off The Record podcast talking about the old site move documentation written by former Googler, Pierre Far.
Go through those changes from the Wayback machine to the new URL or just read the new one so you don't confuse things.
Forum discussion at Mastodon.
