See more or less official solutions in Malware detection prevents Docker Desktop to start #7527 (Docker for Mac Github issue item). Especially for people not having installed Docker via Brew or for a general understanding of the issue. There are also previous issue discussions in the same Docker for Mac account if you're interested in more details. But the solution is in the link.
My solution was to obliterate my Docker install, except my .docker folder, using both AppCleaner and the steps in the linked article, as I really didn't need anything currently in it. Then I just got the latest version.