Smooth Edges In Segmentation

Question

I am working on project in which i have to do segmentation masking. Now problem is that exported masked image should have 2 things.

NOTE: Please download both images for better understanding my problem

1. Only 2 Colors.
2. No Jagged Edges.

Tools Used:

1. Cvat
2. Photopea ( for Reducing Colors )
3. Pixspy ( for checking how many colors image have )

If i achieve 1 ( means if i reduce color ) than for sure jagged edges will appear. because mask is png and if you remove colors from jagged edges than it is obvious that all shades which given illusion of image smoothing will disappear. and if i go with no jagged edges than i will get thousands of colors in image.

Image with Smooth edges but many colors around 12k

Image with Jagged edges but limited colors only 2

How can i achieve both of the things on same time for my mask.