Air Tag not in "Find my" app

I just set up an air tag on my iPhone 15. The IOS software is up to date. The setup went normally, and at the end I was able to see the tags on a map. However when I go to “find my” app there is no air tag, my other Apple prodcts are there. I reset the air tags and went through the set again, 5 times. I check my location setting on the phone. I reset them. I reset the network settings. I changed the batteries in the tags. Restarted my phone. Still no air tag in the find my app. I also went through all of this on my iPad to see if the phone was the problem, but same issue. I just bought this tag and can’t return it.