When I create a new project it's available in the Data & Storage, but when I open existing ones (downloaded from the web), it isn't showing. WebStorage isn't showing either...
Can't I add it to any project?
You said it is available when you create a new project but not in existing ones. It must be because the LocalStorage plugin is already in your project, please check again. You can only put 1 localstorage in your entire project and after you add 1, localstorage won't show up on "Insert object".