I’ve worked on a non-Windows updater as well and discovered the archive by @Jared_Mauch1 who did virtually the same, as well as @Shymon_Samsel and @AlexS tutorials. In order to make plucking the right files a bit less cumbersome, I wrote a script which you can find here:
It will download both 3.17 BIOS and 3.19 BIOS+CSME Updates, and repackage them to be useable. In order to also be able to flash the CSME (which is out-of-date since May '22!), I also included the FWUpdLcl.efi CSME flasher, originally from intel, but from questionable sources. But the shell script won’t download it for you, just give you the URL and will check the checksum. The pre-built ZIP files will contain those files though!
Either way, I hope it’s helpful to you!
Background Info
The firmware of the laptop consists of multiple parts, the BIOS/UEFI firmware proper, the Embedded Controller etc. by Insyde H20 and the CS/ME from intel. For everything related to the UEFI and EC, Insyde provides a Windows installer (up to 3.19) and an EFI Flashing Tool (up to 3.17) as well as, through Framework, LVFS Update capsules (up to 3.06?).
Using the UEFI Flashing Tool from 3.17, we can update our UEFI & EC to 3.19 with the firmware files from the 3.19 Windows release (with a few tricks such as stubbing the FWUpdLcl). Why Framework doesn’t release such an update for at least 3.19 without CSME is beyond me.
In order to update the CSME, we need the FWUpdLcl tool from intel. It comes in multiple forms such as a Windows binary (contained in the 3.19 Windows release), a UEFI updater (not contained in any Framework Firmware update yet, since the CSME was never updated) and a Linux updater (ditto). As such, we need to source this file from sketchy websites 0:-)
Luckily for us, someone has uploaded the CMSE ST for our system which contains both the Linux and the UEFI based CSME updater. We can use either to update our CSME to the latest firmware version provided by Framework.