First thing I noticed, is that you need a common reference to ground between the ESP32 and the Notecarrier. I assume they are connected to the same PC, so that sorta works, but it’s always a good habit to go ahead and connect the GND pins between the two devices.
TX → RX and RX → TX is correct 
In order to correctly interpret the signals coming from the ESP32, the Notecarrier needs to know the logic level voltage of the ESP32. Remember, you are plugged into USB, so the Notecard is operating at 5V. However, the ESP32 is a 3V3 device. In order to let the Notecard know this, you will need to put a line from the 3V3 pin on the ESP32 to the VIO pin of the Notecarrier.
| ESP32 | Notecarrier-AA |
|---|---|
GND |
GND |
3V3 |
VIO |
RX |
TX |
TX |
RX |
Give that a try and let me know if that helps.