When I read BIGTREETECH-SKR-mini-E3/firmware/V1.2 at master · bigtreetech/BIGTREETECH-SKR-mini-E3 · GitHub it says
After the compilation is successful, a firmware.bin file will be generated in the .pio\build\STM32F103RC_bigtree directory. We will copy this file to the TF card of the motherboard, and then reset the motherboard, so that the firmware is burned into the motherboard, the red led D10 will always blink in the burning, After the burning is completed, D10 stop blink, and the file name in the TF card will change from ‘firmware.bin’ to ‘FIRMWARE.CUR’
So have you tried that?
If you want to upload via USB then you have to either use an STLink or put the chip in USB bootloader mode to do a upload via upload_protocol = dfu (has to be selected in the platformio.ini environment). But the way I read it, it should be done via SD card.