I cannot predict how this will work but the idea is to use grub’s boot from ISO functionality.
This should - theoretically make it possible to boot a windows iso of some kind.
The preferable would be a Windows rescue ISO like Hirens Boot CD which uses a Windows Rescue environment - WinRE.
In theory - from that environment and your hardware can be flashed from within windows you should be able to both download and flash the firmware.
Booting a Manjaro ISO is easy-peasy - just read this
Booting a Windows ISO from GRUB is more tricky and frankly I don’t the how to do it but I figure if ventoy project can do it - it should be possible.
I have also been playing with the thought of using the installed Manjaro to manually install Manjaro onto an USB - then use grub efi installer without the removable argument which in theory should add the usb stick to the systems firmware.
If that works then you would have an entry in efi which in theory could also boot a stick with a windows installer or winpe. If this works you could use Manjaro to prepare an USB with ventoy - then one-to-one copy Hirens boot CD to the USB.
But all that is speculation and I have idea if it will work at all.
From a fedora forum - I found this
Which matches my thought of using efibootmgr to create an entry pointing to the USB - if your system only has one disk then pointing to
# efibootmgr --create --disk /dev/sdb --part 1 --loader /EFI/folder/efistub --label 'USB RESCUE'
From an old topic found in the archive
On a note - I vaguely recall someone who fixed in similar issue - the problem was the EFI loader - a wild guess could be a version issue between the loader and firmware blocking the firmware from loading correctly.
Proceed with caution - this is completely unverified - the result may have been sheer luck - but if you still have Windows installed on the system this may work. Please check the contents of /boot/efi/EFI subfolders and files - you need to be root to list the contents - but be careful with this one as it may brick your system. The trick was to remove the grub efistub so the system was forced to use the windows stub - which brought the firmware back to life.