[mothered]

Was there any investigation from Amazon’s side? I am wondering if they do some steps to find the cause.

They'll liaise with the carrier to cross-check the weight of the consignment.

The AirPods are light enough to not register a weight, so there's no cause for concern.

Do they report that on police station?

No, It's a separate event altogether, by way of requesting (you) to file a police report.