I just tested this in my sandbox and the new assignments began as unpublished no matter how I started the assignment. I'm not sure this is normal behavior, or an expected change. However, the module itself can be unpublished, and if the module tab is the only student access allowed, students should not have access to the unpublished content inside the unpublished module.
As an alternative, you can create your assignments on the assignment tab, which opens directly to where you fill in content, where you are in full control of choosing save verses save and publish. Then you can add it to the appropriate module later.
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