@tautech Sorry for asking about "how many beers you would like to have"; I understand that you have never expected many beers from people who need help on this forum.
Update: Jiayu Wu at Siglent HQ has sent the SD recovery package and the firmware update file for SDS3000 series to me, and I restored the SDS3104 oscilloscope's firmware successfully.
I was about to install the TI Code Composer Studio when I realized there are some write-only registers in peripherals like GPMC (this means I shouldn't try to dump the whole register address range of the peripheral with OpenOCD), right before receiving the recovery package. I decided not to continue the effort with the JTAG; however, checking the front and back sides of the mainboard (SDY8.007.045E, ACQ2_131100), the EEPROM wasn't found; It seems like the BTD data can be backed up within the "Lecroy" folder, but the "Restore BTD from EEPROM" in the service menu failed with error. I wish the model data is stored in some MCU or something in the front panel, not in the NAND... Anyway, "Restore BTD from EEPROM" isn't really needed at least at this moment.
Side note: I've seen the "Programming the mainboard microcontroller" message while doing the FLA firmware update.