AI mode runs on a free Google Gemini key that you bring yourself. This is what keeps the AI free with no monthly bill.
Go to aistudio.google.com/apikey and sign in with a Google account.
Click Create API key, then copy the key it gives you. That is everything you need.
Leave billing off on the Google Cloud project. The free tier is plenty for a normal store, and keeping billing off means you are never charged.