Why does my AirTag only work when my iPhone is nearby?

The purpose of the AirTag is to help you locate an item that you may have misplaced. It is not a tracking device.

The AirTag employs a Bluetooth beacon that transmits it ID approximately every 3-5 mins to conserve battery life. As such, it relies on the Apple Find My Network (which consists of literally millions of iPhone) to be able to relay its ID, along with the phone's GPS location to the Apple servers over the Internet. This is where its location updates would appear on the Find My app on your iPhone. Only you can track it.

If your phone is within Bluetooth range of the tag, it should appear on the Find My app on that phone. When outside of that range, it will require the Find My Network to work. The fact that you have multiple Apple devices at home doesn't matter if your phone is within its Bluetooth range.

I guess the question is what were you expecting an AirTag to do for you? Whatever that is, did you do a little research before you bought one to see if it will meet those needs?

Regardless, if it doesn't meet those needs, you have 14 days (from the purchase date) to return them for a full refund ... if you bought them directly from Apple.

AirTag lacks Wi-Fi and cellular communications radios, and geolocation requires relaying AirTag position through another Apple device that happens to be within Bluetooth range. That range is probably ten meters in best conditions, though Apple doesn’t publish AirTag range specs.