There has been a lot of work on coreboot_util.sh, which now works much better in a Qube, container, or off-host.
If you are using PureBoot (with any installed OS), then PureBoot does the real flashing work. You can run coreboot_util.sh to download the new ROM, or you can download it yourself from the releases repo (firmware / releases · GitLab). Just put the ROM on a flash drive and flash it within PureBoot.
On the other hand, if you use coreboot/SeaBIOS (or are switching between the two), then coreboot_util.sh ideally will actually flash the update. If you are a Qubes + coreboot/SeaBIOS user, this is where it might be simpler to use PureOS Live. If you don’t want to do that though, coreboot_util.sh will still prepare the ROM for you in a Qube, with bootorder/serial/etc. Then you would have to move the file to dom0 and flash yourself with flashrom.
So overall, this is much smoother now, especially if you use PureBoot. If you do use Qubes with coreboot/SeaBIOS, you might want to consider trying PureBoot Basic instead, which has the capability to update itself like PureBoot but doesn’t require a Librem Key.
If you do still have issues, or there’s an OS/firmware combination that’s not served well right now, feel free to ping me in a relevant thread or open an issue in the utility repo (firmware / utility · GitLab).