I cannot rearrange pages of a PDF in Preview
The PDF is, somehow, locked against editing.
Here is the workaround I found, to achieve the desired result without having to use a third-party app. The idea is to duplicate the PDF from Preview in a way that will remove the restrictions.
Open the PDF and chose File then Print. In the dialog, chose size and orientation, then click on PDF on the bottom left, then Print to PDF.
Open the new file. It can now be modified at will, like any unlocked PDF.