Google's John Mueller said if you see the Google search results being shuffled around after they are loaded, then it is not Google Search doing that. Google does not "shuffle the search results after they're loaded," he said on Twitter.
I've seen some browser extensions, malware, and other hacks do that to the search results before. But once the Google Search results page loads, it will keep the current search results page as is, unless you click on the page to interact with it.
Jonn added "That sounds like something on your side," like some sort of extension or something.
Here are those tweets:
That sounds like something on your side; we don't shuffle the search results after they're loaded.
— ⛰ johnmu is not a cat ⛰ (@JohnMu) October 5, 2022
So if you see this, first try disabling some browser extensions to see if that fixes things. If not, you might have some larger malware issue.
Forum discussion at Twitter.
Note: This was pre-written and scheduled to be posted today, I am currently offline for Succos.