I was thinking of those that extend to fit the door frame. Like this one.
Ones I seen puts stress on the door frame or the door molding.
If it did not. The OP would not be complaining about the weak door frame.
https://www.amazon.com/Aoyar-Adjustable-Installation-Multifunctional-Strength/dp/B08V1HR2JR
A pull-up bar is pretty helpful for the opposite set of muscles, and they are pretty cheap. You can work through this progression as those muscles get stronger: Scapular pulls → Arch Hangs → Pull-up negatives → Pull-ups → Weighted pull-ups. (Source: Reddit bwf sub, with instructions). The link contains the description of how to do the exercises, and details about form.
My bar is a no-screw installation, so it leaves no damage and is portable. It looks somewhat like this: Pull-up bar.