My question is whether the reason why the SD card does not work with C3 is not a hardware problem, but rather because you are trying to run the same sketch as nRF52.
I think you need to try running the SD card with C3 without sticking to the same sketch as nRF52 to determine whether there is a hardware problem.
File/Examples/Examples for XIAO_ ESP32C3/SD/SD_Test
Does the SD card work?