Arduino Pico doesn't work with ST7735 screen
I found out the problem. I was trying to connect to the SCK and MOSI pins on the back of the Pico. Later research shows that these are meant for programming and burning a bootloader onto the microprocessor.
The Adafruit library allowed me to define my own pins for SCK and MOSI.
Once I switched to using the Adafruit_ST7735(int8_t cs, int8_t dc, int8_t mosi, int8_t sclk, int8_t rst) constructor, it worked after that.