Advice for mounting exercise hooks to a section of drywall without studs
Find and use studs for this.   Dynamic human weight ... moving, vibrating, 200 pounds in motion being pulled to a stop by the wall.  Drywall anchors are not designed for that, nor is drywall.   You want 3-inch lag bolts centered carefully on wood studs or toggle bolts through metal studs and ideally multiple ones for redundancy.
Also I agree with the comment above ... roughly a zero percent chance that you don't have a stud at the door frame and in the corner.  How do you know you don't?   And if it's true, and you do what you said with the plywood etc, you'll just snap off the whole sheet of drywall when you hang from it because there is nothing holding it up other than a corner bead and its own rigidity.