Hide schedule action in some documents

[Laruxo]

Describe the bug

I want to filter out "schedule" actions for some documents. Based on the docs, the intended way is to use action property however it is not available for actions created by plugins (e.g. schedule or document-internationalization). There is also a name property available in development, but it is being minified during the build, so it is inconsistent in the deployed studio.

Expected behavior

1. Now that schedule is a built-in feature, it should have the action property
2. Automatically remove publish and schedule actions for live documents
3. In the types, action property could be made mandatory and changed to string, so all plugins would add it.

Screenshots
Here is the log of actions in the deployed Studio, 2nd one is schedule action:

Which versions of Sanity are you using?

4.39.1

Additional context

There is a related issue about extending document actions which might indicate why plugin actions are missing action property.