How can i install grub loader manually in ubuntu 21.10?

I recently installed ubuntu 21.10 dualboot with windows 10. Grub install failed during the installation and the system boots into Linux automatically. If i boot into the Windows partition with the boot menu it goes to grub rescue. I tried running sudo update-grub and changed GRUB_TIMEOT_STYLE from hidden to menu but nothing happens. Here is a picture of the disk with Ubuntu:

And here is a picture of the disk with Windows:

This is not exactly an answer, because this would not be "manually", but I achieved good results with "Boot Repair". See: https://help.ubuntu.com/community/Boot-Repair

Boot Repair will not repair Windows boot files. When Windows is installed it should make its own EFI folder of boot files, and it is normally about 100 MB in size, which is big enough to include the grub efi files also. Did you install Windows after Ubuntu?

As you have a grub EFI of 4.2GB it is not only a waste of space, but suggests that the Windows EFI has somehow been wiped, and sda6 serves for Linux booting only. So Windows boot files may be missing from sda6, thus Windows won't boot. If you run sudo ls /boot/efi/EFI, is Microsoft shown as a folder? If so, what does sudo ls /boot/efi/EFI/Microsoft/Boot|grep -i ^b show?