I am afraid that VS extension does not use the cloud storage as Windows client does, where to sync your files so they can be visible to the other clients.
However, you can use a third party version control like GitHub and export your project there and then clone
it using for example our Windows client. Thus, you will be able to open the project in any of the other clients.
Notice that you will have to use repository structure as this one
in order to be able to successfully clone the app.