A saved form doesn’t give me the option to send, even after I get the PDF.
To be able to Send a Form, you must have Send permission for the Project.
Ensure the Project Owner or an Admin User (with Access All Projects) has added you as a Project Member with at least Send Records permission.
Permission levels are cumulative, so you can achieve this by either having Send Records or Edit Project access.
Have a look here for how to add or change project members.