BR,
I believe the save/send process, which uses the same logic as Embed Metadata, only updates covers. If the EPUB does not declare a cover, none of these processes will add one. Traditionally you needed Modify EPUB or Polish book to force insert a cover.
Also conversion will add one. It will not use the contents of the input file, it uses the cover metadata in calibre.
When using Add books on PDF, calibre will IIRC use an image of the first page to add as cover metadata for the book record. This will be duplicate content.