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No, it can piggyback on any Apple device that's in Bluetooth range to get its location to you. I don't think there's such a thing as public tracking.
If AirTag is separated from its owner and out of Bluetooth range, the Find My network can help track it down. The Find My network is approaching a billion Apple devices and can detect Bluetooth signals from a lost AirTag and relay the location back to its owner, all in the background, anonymously and privately.
Anyone planning to use airtags as a bike tracker? Can imagine they would be pretty good if they can be hidden inside one of the tubes