Notes that you annotate onto a PDF from Preview's markup are just that — Notes. You see this enabler in the Preview print panel.
Comments are something that you add in a word processing document, usually associated with an author name, and one must enable these comments in the PDF export panel of that word processing document, where they will appear in that exported PDF as a separate column on the PDF. Apple's Pages (e.g. 13.1) has that provision in its export to PDF panel.
With macOS 12.6.7, and depending on the choice of Notes or Comments above, I have no issue producing these on printed output.