My AirTag Bluetooth isn’t working

The battery on one of my AirTags died. I finally replaced it but it’s doing something weird in Find My. It shows the tag is with me but it won’t play a sound when I select that option. Additionally when I select Find, my phone can’t find its signal. I also am not able to rename the tag. I tried restarting my iPhone. I tried restarting the Find My app. And I tried resetting the tag, but reconnection fails because Bluetooth won’t connect. Did the Bluetooth signal stop working in this tag?