Craft Nitro PHP extension ext-zip * is missing
You'll want to run that composer create-project command from inside of your Nitro VM. If you run it on your host machine, it'll use whatever version of PHP your host machine has installed.
Do this:

Make sure Composer is installed in the VM by running nitro install composer from the host machine. https://craftcms.com/docs/nitro/commands.html#install-composer

SSH into the box by running nitro ssh. https://craftcms.com/docs/nitro/commands.html#ssh

Run composer create-project craftcms/craft to get a fresh new Craft project inside the VM.