There are macOS tools able to read the firmware version. Running the updates these tools are used, the firmware updates are staged to the internal EFI and on the next reboot it should run and apply the updates. This does not work in any case and on the first attempt, just retry. You may check the EFI partitions for an APPLE folder containing the firmware.scap files for updates. I could update all my iMac11,x and iMac12,x systems.
Your machine will not get any firmware updates from Mojave, it was never supported to run with Mojave. Why should apple bundle software for unsupported macs into macOS updates?
You need to go back to High Sierra, or the latest supported macOS version in general to get the firmware updates and APFS support.