Ather, trying for 2 hours, finally made him work.
Before showing your way, you can go through this problem once.
By default, babun set to C:\Users\13000\.babun\ . Therefore, we can configure it by redefining the user setting in VS Code as:
"terminal.integrated.shell.windows": "C:\\Users\\YOURUSERNAME\\.babun\\cygwin\\bin\\zsh.exe",
After saving, reload the window and everything will be ready.
You will get something like: 
Hope this helps!
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