Apple has today release a further security update for macOS Catalina, number 2021-006. This is an important and urgent update, as it fixes a vulnerability in XNU in which malicious code could run arbitrary code with kernel privileges. Apple is aware of reports that this is already being exploited.
Full details are here.
Thanks to Ian for pointing out that this is now available as a standalone Installer package, from here.
There is no sign of any matching security update for Big Sur, which may well not be affected. I’m afraid that if you’re hoping that Apple will patch this in Mojave, then you’ll be disappointed, as it now appears to have ceased getting any further security updates.