Unfortunately, the system allows us to perform billing based on a default setting. It is not possible to bill per order differently from the default setting.

We can include any document (even an invoice) in the package as a printout, but this is only possible until the order processing starts:

Place the order in "Stopped" status, then click on "Attachments" on the order page to upload the document to be printed in pdf format. Save, set the order to "Packable" status so that when packaged, the attached document will be printed and placed in the package.
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With the above operation, the invoice will still be sent by e-mail, even if it is the default billing method.