Hello!
Thank you for your feedback.
As we mentioned before, this functionality is not planned because the link to the project is in the web page source and thus embedded projects can be accessed by anyone, which is insecure.
We are now designing the secure solution for cooperative work on the projects. It is still hard to estimate the release date, but we will share any update on the matter.
As for your current issue - we see a potential workaround for it. When working with embedded projects users can download a temporary vector layers that they create during the session of working with the project. What you can do is add an option to upload the .geojson file to your website, so your users can send you their files with annotations that you later can upload to the project. This solution is not elegant, but it should work.