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I'm sorry to hear that you feel worried about your phone.
You might experience that your Xperia device is vibrating when you touch the metal surface during charging. This is due to non-harmful leakage current. The vibrations are not dangerous, and will not affect your device.
As @Viridis mentions, it's not uncommon or specific for Xperia XZ.
@Aithir Have you checked if the device is correctly charging? Is the LED turned on? Normally, it should vibrate first time you connect the phone to charge it.