This change in projected perspective is indeed an important effect well know in photography, but it is actually related to the distance between the viewer and the objects viewed and not the focal length itself.Hi Renze, you are right that both change with magnification but they are quite different. With 'Depth of field', everything inside the depth of field is in focus, and everything outside is not in focus.
With the compression effect, the entire scene can be in focus but nevertheless with higher magnification (or in photography with longer focal length lenses) there appears to be much less distance between objects closer to the observer and other objects that are further away. The pic below illustrates this.
Lee View attachment 1362618
If you were to use the different objectives/lenses to take pictures from the same position/distance, and crop the wide angle picture to have the same magnification as given by the telephote lens, you would end up with the same perspective.
If you want to have the pictured item or person having the same size on the picture with different lenses without cropping, you would of course have to step closer woth the wode angle lens and that will result in the difference between the pictures shown here.
Thus I don’t think this would be the cause of more ‘3D’ effect when using lower magnification binoculars instead of higher magnification ones, unless it makes you step closer or if it would result in some playing tricks with our brain and kind of photographic memory/interpretation of what we see.
I am not 100% sure though: I don’t have lower magnification binoculars than 8x binoculars to check.