I have the Pico 40 pin HAT, joypad & 4-button version of the Waveshare 1.3" 240x240 LCD. The MicroPython demo from the Waveshare web site worked fine on the display but I could not get anything to draw on the display using this st7789py_mpy library. The backlight was on but the screen was black. I ended up checking the SPI definition against the Waveshare demo and noticed that the polarity was set to 0 whereas it is 1 in the tft_config.py (line 29) for the Waveshare 1.3-inch LCD.
As soon as I changed this, all the example programs listed here worked fine.