Add "textmode" to boot params in syslinux.cfg and the OS is forced to boot to a local console instead of Kodi. This allows you to connect a USB keyboard to poke around a look at the system log with "dmesg" .. which will probably reveal the box can see the SDIO module but is missing a firmware and nvram config file to make it work.
The missing files should be in this repo: https://github.com/LibreELEC/brcmfmac_sdio-firmware/ but you'll need to download it on another machine and copy it to the root folder of the USB stick, then boot the box into textmode and copy the files to the /storage/.config/firmware/brcm/ folder before rebooting. On reboot the firmware will appear in /usr/lib/firmware and the card should work.
If you confirm that fixes it, we'll have a think about how to resolve things properly in the normal image.