I have 8 airtags, four of which were indicating low battery. When I replaced the batteries following the 5-6 times insert and replace process, one immediately recognized the battery, one had to be removed from the registry and then added, but two others would not recognize the new battery at all after several attempts. I tested the batteries to confirm that they were good, but the two airtags still would not recognize the new batteries. I know that the batteries were good since I exchanged them and they worked in other airtags. After waiting awhile, one of the airtags finally did recognize the new battery, but I still have one more that does not. Due to the randomness of success/failure of the battery replacement process, it appears there is something going on with the process, software or the hardware that's not documented by Apple.
UPDATE: After scrubbing the "faulty" battery, and reinstalling it, the airtag recognized the new battery. The battery had "bitter taste" child-proofing. Apple needs to mention this on their battery replacement documentation.