You are still a writer. Are you by chance using Fire Fox as your browser? I have heard it doesn’t like Medium all that much. You might be experiencing a glitch.
It is correct that the only way to get in it is through the draft form, even if you do submit it. It will stay there until it is published. Just in case, ‘add to publication’ is not in the ‘publish’ menu, but under the 3 dots next to the ‘publish’ button. Once you’ve added it, Medium will tell you you did so, and it will show up in the middle on top of your draft.