Remove the batteries from all AirTags and leave aside for a bit, make sure you are updated to iOS 15.2, remove ALL bluetooth devices from your phone/iPad, reset your network settings, sign out of your iCloud account on your phone/iPad, then sign back in. Restarting your phone/iPad after sign in seems to help.
Once you've restarted your phone/iPad after the steps above, you will need to clear each AirTag one a time. To do this you remove and replace the battery five times. On the 6th time, put the cap back on and secure the battery. It will beep. Go to FindMy and set the AirTag directly on your phone/iPad screen and go through the steps to add it.
This is what I did to make it work finally. I couldn't use my phone because I didn't want to have to repair my watch, etc. I used my iPad to do it. I noticed on the iPad, that while I was adding them, it was only showing one or two in the items screen. When I looked at my phone, they were all there.
See if this helps! I know it's frustrating, and it seems to be an issue with iOS 15.2, FindMy, and iCloud. My guess is it's an iCloud issue that needs work on the back end. Other people I know have been able to add them with no issue until iOS 15.1 and 15.2 were released.