I reached out to Code.org and this is what they said:
We are not currently taking submissions to the featured gallery, but we will eventually allow all students to submit their projects to be featured. Thank you for your patience while we work to get the new gallery fully functional.
It also links this article for more information.
So apparently the plan is to launch the new gallery now, and add a feature for project submissions later. The projects in the gallery will “rotate periodically throughout the year”, and anyone can suggest a project to feature as long as it doesn’t break the Terms of Service.
And naturally, there’s a catch: projects that are featured cannot be edited until they are removed. This means that if you make a really good game and manage to get it featured, you can’t change any of the code, potentially for several months. The only option is to remix, and then of course it’s not featured.