"Find My" sends notifications to nearby iPhones that a device is nearby (and they can see its tracking)

Hi.

I have a really annoying issue.

I recently purchased an iPhone 16 Pro and shortly after the AirPods 4, both new.

I connected the AirPods via Bluetooth and then inserted them into the Find My app.

Since day one, every iPhone nearby (I have an XS that I use for work) but also those of my friends (there are 2 and they both do it) receive notifications that a device is nearby, and they are able to track the movement via the Find My notification (and in fact track my movement if the headphones come with me).

Also they can trigger the localization sound or navigate to them

Also, AirPods make sound without anyone doing anything (like a notification)

Is there a way to solve this situation?? I have tried to reset the AirPods several times but without success, and honestly the issue seems rather serious to me since potentially any iPhone that comes within range of my Bluetooth sees the notification.

Hope to find a solution asap.