If you want to add a button to the post menu then you’ll need something a little bit different since posts are widgets.
You would need to add something like this to your theme / plugin.
api.addPostMenuButton("my-button", () => {
return {
action: "someAction",
icon: "someIcon",
className: "someClass",
title: "some title",
};
});
The plugin API has a method for adding new buttons that makes this relatively easy.
This theme component uses that method to add a new button to that menu based on some conditions and defines a new action, so have a look here