Howto repair broken USB-C Power Delivery cable?
USB C is a dense pinout connector and Power Delivery requires more than just the "standard" USB 2.0 pins of Data+, Data-, 5V and GND.
From EE: How does a USB C port provide the power to charge laptops? you can see that the CC1/CC2 pins beside the D+/D- pins are used to communicate for USB PD.
This is the main reason why Power Delivery does not work for Type A ports, because they lack the communications lines necessary for negotiation and as a result revert to the "old" power level being selected by specific resistances across the USB data lines trick.
You need to find out if these pins are wired up in your new connector, if they are not then Power Delivery using that connector will be impossible.
The cable with the plug you want to connect is not a suitable replacement. It is a loose USB-C 2.0 cable with a power line and a D + D- line without the PD (Power Delivery) function.
You must use the appropriate plug. Search alliexpres under the name "Welding wire type USB C to Type-C PD plug 100W 20V 5A Quick Charge connector Fast Charging Cable power Data adapter With case"
Source of Aliexpres photo :
An exemplary connection diagram :