Airtag not pairing after battery replacement

I replaced the battery today on my AirTag, after testing the one I've had in for nearly a year and finding it to be almost flat.

I got the little chirrup from the AirTag that it was working with a fresh battery installed, but noticed that it had gone from my 'Find My' app. I clicked on the blue plus symbol to the right of 'Devices' and clicked add AirTag, but after a few minutes of leaving the AirTag right next to the phone, my iPhone XS would not see it and tried to reconnect several times with no joy.

I've been through some help articles and restarted my iPhone, tried another battery in the AirTag (both tested and on full power), reset my Network preferences on the iPhone, toggled off and back on after a restart the Location Services, made sure Two-Factor Authentication is Enabled, (yes) Mobile Data is running and still my iPhone cannot see the AirTag that had been working for nearly a year!

Any suggestions would be great, cheers!