GoJS is purely a presentation layer library for building displays and editing tools of visual diagrams. There is no “file type” for storing GoJS models. There is no expected or required connector to any particular database system.
GoJSModels do make it easy to read and write models in JSON-formatted text. You can see many examples of this throughout the samples, where there are “Save” and “Load” buttons that write to and read from the page itself in a textarea element. But each sample has its own custom ad-hoc “schema” that is easy for you to adapt by adding or renaming or removing properties. Models are just organized collections of JavaScript Objects, one per node or link.
Depending on how your web app is organized, you will want to use its web services or web api or other mechanisms to communicate between the HTML page and the server.