Shoppers can ask for texts about their order at checkout (Text me updates about this order). Choose which updates go by text in your store's Team › Customer emails, under Text messages: order confirmed, on its way (with the order link), delivered.
Each text names your store and says how to stop (reply STOP). Each text uses a few AI tokens from your plan. Latest texts shows what went, with only the last digits of the number.
If text messages aren't switched on for your account yet, the screen says so: your choices are kept, and shoppers aren't asked until texts work.