Mine did this early on - my keys a few times as I wrote about, and my bag once. Now however, this has not happened in a number of weeks. So it appears to have cleared up somehow.
This seems to have occurred for a few of us but, based on the few folks on this thread, doesn't seem like it's very common. Trying for a theory, I'm wondering if we share a common characteristic with respect to Apple which caused this to happen to us? I have two apple IDs (which is a constant hassle). I have my original Apple ID for "media and purchases". I have a second Apple ID for iCloud. When my keys were chiming, it was almost like it didn't know I was me, so to speak. I wonder if there was some confusion about Apple ID association with the AirTag, and then this somehow got fixed. I think my AirTags should be associated with my iCloud ID (although I don't find a way to really verify that). Just a theory, but I thought I'd add this to the thread in case we share having multiple Apple IDs in common.