The Publish button in the new editor isn’t exactly the same as the old one it seems. It allows you to specify which branch(es) will be published and where.
To actually publish a commit from the master branch (or any other version system you want to come up with) you can merge your commit into the published branch.
Here is the relevant docs page:
I’m still getting used to it myself, and honestly I’m not a big fan of Git. It’s powerful and also powerfully unintuitive.