"Searching for Signal" & "Connected Signal Weak" & AirTag can't be located until I'm almost on top of it.

Bought a new Apple AirTag & connected to my iphone 13. In spite of strong cell & Internet signal, repeatedly receive message "Searching for signal..." and "Connected Signal is Weak". And the device can't be located until I'm within 13 feet. Even when it does locate the AirTag, the Find Me app sends me in the wrong direction. If I didn't know where the device is, & in a completely quiet location, I'd never find the AirTag. I've replaced the battery & that didn't help. Is this a faulty Tag or a compatibility issue or something else?