There's no internal markdown file. When you press the export button, it gets generated from the HTML content of the editor. The extension saves the state of the editor in browser's local storage. I don't think it's possible to access it outside of the extension itself.

There is a Firefox add-on, if you visit the site from Firefox, it should point you to the Mozilla Add-ons page [0].

[0] https://addons.mozilla.org/en-US/firefox/addon/nutab-new-tab...