I found this blogpost in the community forum where it is stated by a Framework Team member that Framework only recommends updating the BIOS via the EFI updater due to some limitations of LVFS:

https://community.frame.work/t/13th-gen-intel-core-bios-3-05-release-and-2024-06-25-drivers-release/53641#linuxlvfs-7

Reading the official Framework documentation concerning BIOS updates this circumstance is not mentioned anywhere:
https://knowledgebase.frame.work/en_us/framework-laptop-bios-and-driver-releases-13th-gen-intel-core-BkQBvKWr3

I'm wondering is the statement still true? If yes, I suggest mentioning this on the official BIOS update document. At least I would want to know and I guess the fewest people stumble over the community forum blog post.

Apropos: I love it that firmware updates are available via LVFS. Thanks for the good work!

Cheers, Marten