Thank you so much for your many replies!

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

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.