Transforming a group is great for adjusting the perspective of many elements like they’re a single element. In situations where all the selected elements should be transformed identically, but individually the approach is slightly different.
Rather than selecting an entire group, click into a group (if they’re in a group) and select all the elements at once by holding SHIFT while selecting. As elements are selected, the Gizmo will transition to stay centred over all the selected elements.
Now, when transforming the objects, they won’t stay on the same plane as they did before, they’ll actually all transition around their own points of rotation, creating a much different effect.