There are a few problems with tracking a cat with an Airtag so - required proximity to iDevices, wearing a collar with a coinsized Airtag, and that AirTags are designed to sound off an alarm when they’ve been separately from the owner for a period of time.
Be careful tracking cats. They get up to all sorts of things you might not like, and frequently visit other houses to scrounge food. Sometimes ignorance is bliss.