How to apply an orientation transform to smooth vertices?

Hello, I have been studying blender and 3d modeling for about a month and ran into a problem. The orientation transform does not affect the smooth vertices.
For example, an orientation transform is applied on Move / Rotate / Scale (Fig. 1, Fig. 2).
But the smooth vertices always uses the local orientation and the Z-axis of the normal orientation is not applied, the Z-axis of the local orientation is used (Fig. 3).

Is there a way to apply orientation normals to smooth vertices? (What would have happened like this (Fig. 4)).

If the blender does not have this function, perhaps you would advise an Addon for this?

I usually use smooth vertices for a quick and dirty fix on a dense mesh rather than a precise modeling tool. In a case like this, I’d go with edge slide or something.

If you really need this feature, you can post it on rightclickselect.