I've recently looked into fixing this issue, and came up with a consistent way of restoring the laptop to full operation.
The boot menu entries can be partially restored by bridging the "CL1_CL2" test point that is located under or next to the RAM slots.
It may be required to have the laptop powered (or even powered on) while bridging the contacts for the test points to have any effect.
This brings back the device-based boot menu entries, but does not yet restore access to the BIOS Setup menu.
For that, a USB stick with Fujitsu's BIOS update tool (search by serial number to make sure you find the correct hardware revision) needs to be prepared, booted from, and run.
This restores most BIOS settings to their default, including the missing BIOS Setup menu.
Alternatively, if the currently installed Linux system is still bootable (I know this doesn't apply to OP, but maybe others end up here and still have a bootable system), one can use this tool to restore all entries without having to go through a BIOS update and reset.
This works by manually rewriting all broken EFI variables with their expected content.
Please do make note of the list of supported configurations and of the disclaimer (and let me know in case the tool does or doesn't work on some previously untested configuration).
In case you want to know more about this works, there is a post explaining the underlying details.
Lastly, a workaround for the issue has been merged into the Linux kernel, which should keep this from occurring on any new installations.
This patch already ended up in the current installation media for the Ubuntu 24.04 beta (which I have confirmed to be not affected), and it will presumably be included in all installation media going forward.