I use MacOS Monterey. The "at" command exists, but some kind of security permission seems to have changed making the command appear to function, but it doesn't actually run the script that you schedule. For this purpose, that's a harmless feature, because we're only running "at" to convert the time.
I'm very surprised that you say "at" doesn't exist in Big Sur. That would mean Apple removed it and put it back in after it was deprecated. Instead, I would speculate that your path may have been modified making "at" unavailable. Or maybe "at" is a built-in shell command and you are using the wrong shell.