Add Windows Boot Manager to GRUB on live USB

Question

The focus of the question is not How to add Windows boot entry to GRUB or Ubuntu boot entry to Windows Boot Manager, but the "on live USB" part.

OS Prober is no longer ran by default as of nowadays grub. So I

• added GRUB_DISABLE_OS_PROBER=false to /etc/default/grub as per here.
• and redo grub-install as per the answer given at Cannot update grub with parameters on live USB

However, I don't see grub-install giving output of adding Windows Boot Manager, and I don't see any /boot/grub/grub.cfg file get generated.

Running both update-grub and grub-mkconfig will give the error:

/usr/sbin/grub-probe: error: failed to get canonical path of `/cow'.

Fixing boot problems with live CD/USB is a common practice, but this error blocks me from doing it.

What's the fix please?