Have you tried a different SD card?
Have you been able to format the SD card on a PC?
Can you read data from a text file on a formatted SD card, using the shield?
It appears the sd card isn't pushed into the slot completely. Was that intentional?
Edit: And you don't have the icsp connector installed. From Adafruit
As of Aug 20, 2023 - we've updated this PCB with Adafruit Pinguin to make a lovely and legible silkscreen and it now uses the 2x3 dedicated SPI port instead of pins 11, 12, 13. This makes it compatible with a wider range of Arduino-shaped boards!