How to add a Service to Accessibility permissions
Here's the roundabout way I achieved it.


In Automator write your application, and save it as an Application (foo.app)
In Automator, create a separate Quick Action. Get that Quick Action to launch the previous Application you created (launchfoo.workflow)
System Preferences > Security &amp; Privacy > Accessibility: Add foo.app to the permissions
System Preferences > Keyboard > Shortcuts > Services: Give launchfoo a shortcut