com.automator.runner.xpc is not allowed to send keystrokes
I have solved this issue recently in case anyone is interested in how. It is NOT actually necessary for System Events to have direct Accessibility privileges. What you need to add are a total of 3 apps, Automator, Script Editor, and AppleScript Utility.
The Automator and Script Editor apps are found within the ~/Applications and ~/Applications/Utilities folders, respectively. What is harder to find is the AppleScript Utility app, seen below:

To add AppleScript Utility app, click the + button on Accessibility, then navigate to (a shortcut is CMD+SHIFT+G)
/System/Library/CoreServices

then open the application called AppleScript Utility.
Afterwards, run a script in automator again, which updates the privileges and things should run well after. In summary, Automator, Script Editor, and AppleScript Utility need to be added to Accessibility.