Hello Misaki!
I studied your setup a bit, I think yours is a nice solution overall. HEre are some small suggestions:
You could adjust the weights of these two vertices here to make a smoother curve:

You could add a couple more points too if you feel the border is too geometric.


If the vertices are tightly close to the mesh, the bending result is better. The same goes if you start with a straight mesh vs a curved mesh. To avoid this:

I tried to do a different setup, but I ended up liking yours better. specifically, I tried to rig the cape first, then duplicate it with its bones, replace the image with the red cape one, parent the duplicated bones to the original bones, and move the duplicates to make the red show from underneath. But as said, I like how you did it 😃