Can I autopopulate between different users' forms with Rules and Webforms or EntityForms?
If I were to approach the problem, each project would be a node.


First install the Field Collection (documentation) and Field Permission modules.
Create a new Content Type (admin/structure/types/add) and call it Project.
Assign the fields you want filled in (admin/structure/types/manage/project/fields).
Add an additional field called Project Status of type "Field Collection" and choose "Embedded" as the widget type. Click save, leave Hide blank items checked on the next page, then click save again.
Go to the Field Collections page (admin/structure/field-collections). You'll see your new Project Status field listed. Click "Manage fields" and add your subform fields here.
At this point, your manager should be able to create new Project nodes, and the Project Status field will hold the additional information. You'll need to set up the field permissions so that the staffer role can only edit the Project Status field.

Back on your node fields page (admin/structure/types/manage/project/fields) edit each field. Near the bottom of each field's settings, look for the Field visibility and permissions section. Choose the Custom permissions radio button and look at the settings available. For your project, you want to allow your staffer role the ability to edit anyone's value for the Project Status field, but none of the other fields.
Remember to also set permissions to allow the manager role to create Project nodes, and the staffer role to edit Project nodes (admin/people/permissions#module-node).


As an added bonus, you can set the field settings for the Project Status field to allow an unlimited number of values. This would allow for updated status as the project progresses. YMMV of course.