No, this function is not available in Airtable API. Therefore, it's not possible to support running an Airtable script by miniExtensions or other 3rd party developers. It’s an internal function limited only to Airtable.
Workaround
The other solution is to trigger the script using Airtable Automation instead of a button click. For example, you can have a checkbox field or single select that would run the automation when its value is updated.