I'm not sure about using the extension APIs, but you can do this through your user settings file (which extensions should be able to change since the "Vim" extension does this, as indicated in my comment above):
→ →
settings.json:
// Place your settings in this file to overwrite the default settings
{
// Controls the cursor style, accepted values are 'block', 'line' and 'underline'
"editor.cursorStyle": "block"
}