Maybe the problem is not caused by hardware or chip. TWR board has openSDA. It's default application is PEmicro. Can you use openSDA to debug? You also can change openSDA application to jlink.
Please take care of those jumper and power supply.
The TWR board can use OPENSDA to flash and debug.
So you can see I remove the OPENSDA jump connect and try to use MCU Link to flash.
It just show can't connection succeeded.
I tried to use MCU-Link on TWR board just like you. It works fine. Since opensda can erase/program KM34, could it be the MCU-link problem? You can try to replace openSDA's application to CMSIS-DAP and try again. Please refer to this link to see how to update openSDA firmware.