Yes, you need to connect the touch pins. In your setup the extra connections would be:
T_IRQ - no connection
T_DO connect to ESP32 pin 19 (MISO)
T_DIN connect to ESP32 pin 23 (MOSI)
T_CS connect to ESP32 pin 13
T_CLK connect to ESP32 pin 18 (SCLK)
Run the Test_Touch_Controller example to test the touch controller interface.
Make sure your display actually has a touch screen film fitted and the XPT2046 controller chip fited as well. Note that some displays sold have the XPT2046 fitted but do not have the touch sensitive film fitted to the screen.
I've included photos of the chip and the film, I hope it's all right, right?
Do I need to add the connections you recorded?
Or do I have to remove the connections that exist for the display, and instead connect them to the touch pins?
Yes you need to add wires to connect the ESP32 to the touch controller on the TFT, leave the existing connections to the TFT otherwise the screen will not work!