Can you put an action (button) in a form? I can see my action in other view types but not a form
No, you cannot; I believe considering actions do tasks like changing columns values or going to different views, etc. it would be confusing if such events happened while you are in the middle of editing data in a form; it could lead to unstable/unwanted states; for example what would happen to the current row you were editing? Should you save? Or should you abort and continue with where the action takes you?
Furthermore… the way you can trigger an action in a form is the option “Event action”. It means you can trigger that action when you save the form. You can find it from the Form view’s definition.