This is because the Site Pages library still uses Content Types. The other 'New' menus on the start page and from other pages don't, they use the new page templates functionality.
Reading between the lines, if MS haven't implemented a consistent 'New' menu option for pages in the Site Pages library it's maybe because content types for site pages are going to ...
Can you check the document properties for an Office file and a non-Office file?
This will return an XML response. Check if the sensitivity is present for both file types.