How to change default integreated terminal in VS Code to kitty on Linux

Question

I'm using kitty (it's a terminal) on Linux, and I want it to be used in VS Code as default terminal (which appears when I click Ctrl+`). Right now VS Code uses its own terminal with name "vscode".

I tried modifying settings by adding there "terminal.external.linuxExec": "/usr/bin/kitty" but it didn't help.

When I click Select Default Profile it only allows me to choose between zsh and bash.

How do I change default terminal to kitty?

UPDATE: I've added kitty profile like so

"terminal.integrated.profiles.linux": {
    "bash": {
      "path": "bash",
      "icon": "terminal-bash"
    },
    "zsh": {
      "path": "zsh"
    },
    ... other profiles

    "kitty": {
      "path": "/usr/bin/kitty"
    }
  },

But when I choose kitty now, it opens the terminal outside of VS Code.