Is charger with USB C connector and 13V output in line with standards?
13V is a very unusual voltage for a USB charger. The only way to achieve it within the USB standard is to implement USB Power Delivery 3.0 plus PPS (Programmable Power Supply), which allows to change the voltage in small increment. Even then, the maximum voltage would either be 12V or 20V.
This charger could still be safe if:

It initially delivers 5V only.
Detects that it is connected to this specific tool and then increases the voltage.

However, I've seen web pages stating that it constantly delivers 13.2V. With a multimeter, you should be able to verify this claim.
If it is true, then this charger is very dangerous for all USB hosts and devices with a USB-C port. Watch out.