2nd time an item had an AirTag, we lost it and AirTag didn’t help. Can someone field some nuances?

Have an AirTag on my keychain. Wife & I both have iPhones.

Been looking for the keys for a week, using another set of keys.

Realized we have an AirTag on keychain. Looked at find my and it showed the keys in our house, but last reported back on 1/25/26 at 5:12pm.

I’d think if I took keys with me out of house (always have my phone), its last location wouldn’t be inside the house?

Since it’s not reporting its location, I’m thinking:

Battery died? But don’t recall getting alerts. Can’t see battery level of AirTag in find me, right?

The AirTag got crushed / destroyed? Again if I took keys w me and dropped it on driveway, the min - 2 to do that till it got crushed,, find me would not update in that time?

I dropped them outside and the 20f temps we’ve been having have froze / disabled the battery?

And with our first failed attempt to find my wife’s purse that had an AirTag…. Is the location of an AirTag in find me the location of the iPhone that reported the AirTag? Or the AirTag itself (I feel it’s the former - AirTag doesn’t have gps. So when a passing iPhone ‘talks’ to the AirTag & reports a location, the best the phone can do is report its own location? I’m 99% sure my wife’s purse was in a group home for men - at first it was reported at the front door of the house (when a resident got driven home from working at the store she lost it in). But as I walked around the house, an occasional update showed it on the 2 roads the house was on the corner of (people with iPhones drove by and AirTag reported in? Me on ground close to house didn’t pick it up).