Apple has recently posted a downloadable Installer package containing Catalina Security Update 2021-001, which was released via Software Update a week ago.

This package is now available from here.

Mojave Security Update 2021-001 is now available as a standalone update from here, and 2021-002 from here.

Apple has made this available for download at some time after 2300 UTC on 8 February 2021. There are some remaining oddities about that, though: the date given on that webpage is 5 February 2021, although the page wasn’t made available for 3-4 days after that date. What’s more, the Installer package containing that update is dated 15 January 2021, two weeks before that urgent security update was released via Software Update on 1 February 2021, and three weeks before its release as a standalone installer package. Doesn’t time seem to fly?

Many thanks to Ian, who kindly let me know of this, and to @HackintoshHD for the info about the latest installers.