The limitation here is that Photoshop does not transform pattern overlays with their associated objects.
You must merge or "bake in" the pattern and then transform the object if you wish the pattern to transform as well. Or you can convert the layer with the pattern overly to a Smart Object layer, and then transform the smart object. This will allow you to further edit the smart object contents if necessary.
Note how the pattern never changes until I merge the layer with the pattern overlay with a blank layer.
So if you want a pattern in Photoshop to conform to a transformation, it can't be a "Pattern Overlay" layer style.