As reported by GiuseppeCM, since Apostrophe 2.102.0, POSTing a piece with apostrophe-headless will leave it unpublished unless you explicitly specify published: true, even if the default for published is true, which is typical for pieces.
This bug also causes other fields to default to undefined rather than their proper default values, so it was a significant problem for headless users.
This bug has been fixed. You must upgrade both apostrophe-headless and apostrophe to get the benefit of the fix.