Public Freakout

Air Tags have a battery and have short-range low-energy communication with phones. What makes them work out-of-range of your phone is that their signal can be picked up by any phone that participates in Apple's tracking network. Say your luggage has an Air Tag in it, and it ended up flying to a different city than you. Your phone obviously can't find the Air Tag because it's out of range, but someone in that other city is bound to have an iPhone. Their phone sees the signal from your Air Tag and reports that location back to Apple's servers. Apple updates the last known location of that tag. You check your phone to see where your luggage is and your phone requests that info from Apple's servers. Apple sends your phone that data, and now you can see your luggage ended up in Timbuktu while you're in Seattle or wherever.