Update-grub does not read /etc/grub.d/40_custom

I’ll refer you to Welcome To Support And Help or the Start Here page, which states

Your provided paste contains only details of non-Ubuntu systems, so why ask here?

FYI: After changing the file you mention; you need to cause the grub configuration used to boot to be re-created with additional entries you’ve added, I didn’t see where you mention doing this.