Yes, SWD is for "Serial Wire Debug" to programm the STM32.
The SD Card is wired directly to the STM32 so it should work as soon as the preenfm is powered without any jumper condition.
Can you resolder the 4 pins on the top to the TFT/SD card, these are responsible for the SD connection.
Then you can try to check continuity between the 4 points (1,2,3,4) and the other side on the top of the TFT PCB with a multimeter.
If you have 2 TFTs, you can also try the other one.
And also try another SD card (but i'm 99% sure that does not come from the SD card).