I am looking for a way to somehow apply a transformation (stretching, rotation) of an image in one layer to a similar image in another layer.
If you "link" both layers (link icon next to the eye icon in the layer list):
then a geometric transform applied to any of the linked layers is applied to the other linked layers (this happens when you confirm the transform, the WYSIWYG adjustments is done only with the active layer).
Linking works for layers in the same image. You can also link paths and channels (between them, or with layers...).