MacOS >11.0: Is there a way to programmatically give an app Privacy->Accessibility Permissions?

I don't think so. Using the tccutil command only allows you to reset the permissions so the user can click and grant permission.

However if the Mac is enrolled in a Mobile Device Management system, you can create a profile that has the appropriate TCC permissions set and push it out to the device. More information here:

https://derflounder.wordpress.com/2018/08/31/creating-privacy-preferences-policy-control-profiles-for-macos/