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.
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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.