I've been experimenting with the GraphiQL interface and it doesn't appear that there is any way to tell if a module is published. There is a state field on assignments, but I can't find one at the module level. Is there a way to find out if a module is published?
I don't see it under the GraphQL interface, but it is available through the REST API for Modules. If you list modules or show module, it has a published property that is true when the module is published and false when the module is not published.
Not all functionality is available under the GraphQL interface and, the last I heard, there was not going to be an effort to go back and make all of the REST API functionality available there. It's mostly as new development happens that you see movement on the GraphQL side.