Catalina: Allow apps to control other apps: Empty list

For some of the items in this System Preference pane, there is no + option to manually add an application. Automation is one of those. When you first open an application that can be used in this way, there will be a request for you to enable it and then you will see it listed in this System Preference pane with an option you can select (check box) to allow it to control other applications.

I believe that for this to work as an app, the MacOS requires the app to use specific Apple-provided developer tools to initiate the change to the Security and Privacy Preference Pane, and without that being implemented properly, it won't let the app control the finder. After all, an app could be downloaded from almost anywhere and thus do harm. Apple probably considers a script that you create more like you simply doing things inside the finder (or in terminal) in person, so its' allowed.

I am not knowledgable enough about AppleScript to know how to do it, but there might be some commands you can include that do set up Security and Privacy the way you want.