This is a simple PHP assignment, really.

Softaculous has an Auto Install API example, which is about 15 lines of PHP for each app, at https://www.softaculous.com/docs/api/auto-install-api/

The app ids are passed as integers, like in the example, WordPress is 26.

A full list of Script IDs is here : http://api.softaculous.com/scripts.php?in=serialize

It looks to me that the action is to simply scrape the Softaculous app list and find the IDs and make an array, and loop over the array, calling the example for each app, inserting the lcase appname into the folder variable, etc.
If we could control the name of the database as the appname, ideal.  Otherwise, capture the database name somehow, and associate it to the app.  At the end, we should end up with a file AppNumber, AppName, FolderName, DatabaseName.

The job will be done when the apps are installed on my new cPanel account, and I can access all the databases through PHPMyAdmin.

===Here is what I wrote previously, a little overly technical, represents the bigger picture, but only the last line still applies.

At minimum, the ones included in Softaculous Free.

First as a cPanel backup which I can restore to a cPanel host, 

OBVIOUSLY, there would need to be a single user with full control of all the databases.

Second, maybe, as a batch file that I could restore on my VPS or in a Docker container.

I don't need the application's files.

I think that for someone who can automate cPanel, this should be fairly easy.

Let me know in your proposal what you plan to deliver, please.