ESP32 with Lolin 2.4 inch TFT Shield Power control
The backlight of this shield is ON as long as there's power on the 3.3V pin, unless you make GPIO 32 an output and pull it low.
In deep sleep, however, GPIO 32 will stop acting as a pulled down output pin but the esp32 keeps its 3.3V output pin powered, so the backlight will switch ON.
You could power the display over a mosfet, controlled by a GPIO.