To disable Copilot in VSCode, a couple of things need to be added to the settings.json:

{
  ...
  "chat.commandCenter.enabled": false,  // disables the chat icon in the top bar
  "chat.experimental.statusIndicator.enabled": false,  // disables status indicator in the bottom bar
  ...
}

Thanks to Chris for his post.

PS: I need to find how to disable it completely. Maybe switching to Codium is already a better choice.