Thank you so much for your many replies!

Only one connection was necessary, i.e. USB C

This depends heavily on the power consumption of the notebook. An HP ZBook is a more powerful mobile workstation that often requires more power than can be supplied via a single USB-C/Thunderbolt cable. Thunderbolt 3 and 4 usually deliver a maximum of 100 watts, which is sufficient for many business notebooks such as the HP EliteBook.

But a ZBook can require 150W or more depending on the model, so the additional power supply is mandatory. If a docking station is in use, it could possibly provide more power, but often this is not enough for a ZBook with a high load.

No, the round jack plug is only used to power the laptop. It depends on the laptop how the power supply is intended. I bought this because I was convinced that the second cable was an aux input.

For the dock to work properly, only a USB-C cable is required for the main connection. However, to take full advantage of features such as charging and extended connectivity, we recommend using the cable supplied by HP, which is designed to support both Thunderbolt and USB-C specifications. Both cables are not absolutely necessary for basic use, but may be useful for certain configurations or advanced features.