Thanks a lot. That makes it work. So for other people that have the same problem the code is:
#include "soc/usb_serial_jtag_struct.h"
USB_SERIAL_JTAG.chip_rst.usb_uart_chip_rst_dis = 1;
USB_SERIAL_JTAG.config_update.config_update = 1;


I might suggest a little more details in the documentation ...

Yes it is that device and I am using the correct connector.
Using pyserial under linux I can toggle the RTS/DTR lines and I can see the change on the device with the same register that contains the USB_SERIAL_JTAG_USB_UART_CHIP_RST_DIS bit. I also see that bit value change. I do the reading with ...

On windows, when the software disconnects from the serial port, it toggles the DTR line which resets the ESP32C6 (I have a esp32c6 devkit mini, v0.0).
I know there is nothing to do on the device for the USB to UART connection but on the USB Serial/JTAG, the documentations says:
Note that as ...