From:
https://manuals.info.apple.com/MANUALS/2000/MA2000/en_US/airtag-AM03403491B-info.pdf
Battery
AirTag contains a coin cell battery. The battery may need to be replaced during
the life of the product. Replace only with the same type (CR2032) and rating of
battery, observing the correct polarity.
To replace the battery:
1. Push the battery compartment door, then turn counter-clockwise with two
thumbs and release when rotation stops.
2. Remove the door.
3. Remove the battery.
4. Insert a CR2032 battery into the device with the positive side (+) facing up.
5. Place the battery compartment door on the device, and rotate clockwise
while gently pushing, until it drops into place.
6. Push door into device until it stops, then rotate clockwise with two thumbs
until rotation stops.
It appears you don't twist the battery, you screw in the door.