I sometimes use a power pack (battery) to charge the battery in the camera via the USB connection.

Thanks Olaf.Good to know.

Welcome. You can use a wall charger for USB charging. 

Can the inserted battery be charged by connecting the camera directly via a USB-C cable to a wall charger, which is generally used to charge my smartphone? Or will it damage the battery/camera?

Thank you very much, sorry for late reply.