Hello Caragrimaldi,
Because I have the same problem I discover some airtags have a bug. At least 3 of my 4 airtags had this bug (not sure for the last because I think I apply the "solution" before detecting was buggy).
Even if my airtags were detected by an iphone 10 kilometers away I was still notify that the airtag is "at home, now, 0 kilometer".
The solution provided by the support is to remove the airtag from your account and add it again. After that, miracle, if my airtag is not detected by anybody i have at least the date and his last known position (and not always now and 0 km) and if my airtag is detected at the swimming pool it appears at the swimming pool.
Unfortunately I am unlucky because I discover this bug after struggling to understand why my lost cat appears to be at home. And because it is lost I could only be able to remove the airtag but could not add it again to my account to solve the bug.
So every day I have notifications that my cat is detected but I don't have the location to go checking if my cat is stuck somewhere, kidnapped, or dead... And support can't help. They can't know the position of the airtag, they can't know if is detected by the same device, they can't simulate a remove/re-add on my account, they can't ask a developper to correct what might be an error in a database to make my airtag work correctly. They can't do nothing except explaining me how to use a not bugged airtag. :-(
My only hope is when I seek my cat early in the morning, some day the notification I will have means that it is MY IPHONE that detected the airtag 10 meter near me.
But a day the battery will be empty and I will not receive notification for my cat anymore...
To lost an airtag, incredible...