1. Select the image you want to apply (or the rectangle/shape it is masked with).
2. Ctrl+C (copy)
3. Select the image or shape you want to apply it on.
4. Ctrl+Alt+V (paste appearance).
The image is basically set as the "Fill" color of the shape you are copying from. So you copy that 'fill' and apply it to another shape. The image will try to fit the new shape, so you shouldn't have to fiddle with it too much.
A minor annoyance with this is if you have rounded corners or shadows on the shape you are applying it on (replacing), they will get removed and you will have to set them again.
as you mentioned, this will also copy all other stylings. Which is another massive anoyance of XD, when you just want to copy the dropshadow of an object without also changing the fill and other stylings.
I whish Adobe could focus more on ease of use and basic functions, instead of adding gimmick features like 3D transform.
Yeah, that has been the general direction for quite some time. It hasn't all been gimmicks, but unfortunately there are quite a few features which in my opinion (and clearly many others) have very few and highly niche use scenarios.
For styles, I wish they took the CSS approach, and we could style groups of elements with classes for example. But we can only hope 🙂