I understand you're looking for the Publish button to update your published project.
If you're not seeing the "Publish" button next to the "Share" button, please try the following:
Click the "Share" button
The modal that appears is split into two sections — in the lower "Publish" section, click "Update"
The help article Update a published functional prototype or web app doesn't seem to explicitly mention this at the moment, but it appears this is one way you can update your project, based on what I was able to test on my end. I'll pass this feedback along to our team internally.