Why do I have to execute `grub-install` and `update-grub2` both internally and externally in `chroot`

Question

I am installing grub to boot the system. Why do I have to execute grub-install and update-grub2 both internally and externally in chroot, otherwise I won't be able to enter the grub interface and will instead enter the efi shell interface?

Burning.sh:

#!/usr/bin/bash

current_path=$(pwd)

hdstr=/dev/sda
hdstr1=${hdstr}1
hdstr2=${hdstr}2
hdstr3=${hdstr}3

root_path=/mnt
boot_path=${root_path}/boot
grub_path=${boot_path}/grub
efi_path=${boot_path}/efi

lib64_path=${root_path}/lib64
bin_path=${root_path}/bin
lib_path=${root_path}/lib


    
execute_command() {
    local command=$1
    eval "$command"
    local status=$?
    if [ $status -eq 0 ]; then
        echo "run the cmd:$command success"
    else
        echo "failed to run the cmd:$command" 
        exit 1
    fi
}

copy_tool() {
    execute_command "sudo cp ${current_path}/grub-install /sbin/"
    execute_command "sudo chmod 777 /sbin/grub-install"
    execute_command "sudo cp ${current_path}/update-grub /sbin/"
    execute_command "sudo chmod 777 /sbin/update-grub"
    execute_command "sudo cp ${current_path}/update-grub2 /sbin/"
    execute_command "sudo chmod 777 /sbin/update-grub2"
}

change_root() {
    execute_command "sudo mount --rbind /dev  /mnt/dev"
    execute_command "sudo mount --rbind /proc /mnt/proc"
    execute_command "sudo mount --rbind /sys  /mnt/sys"

    execute_command "sudo mkdir -p ${bin_path}"
    execute_command "sudo mkdir -p ${lib_path}"
    execute_command "sudo mkdir -p ${lib64_path}"
    execute_command "sudo cp /lib/x86_64-linux-gnu/libtinfo.so.6 ${lib_path}/"
    execute_command "sudo chmod 777 ${lib_path}/libtinfo.so.6"
    
    execute_command "sudo cp /lib/x86_64-linux-gnu/libdl.so.2 ${lib_path}/"
    execute_command "sudo chmod 777 ${lib_path}/libdl.so.2"
    
    execute_command "sudo cp /lib/x86_64-linux-gnu/libc.so.6 ${lib_path}/"
    
    execute_command "sudo cp /lib64/ld-linux-x86-64.so.2 ${lib_path}/"
    
    
    execute_command "sudo ln -s ${lib_path} ${lib64_path}"
    execute_command "sudo cp ${lib_path}/* ${lib64_path}/ -ra"
    
    execute_command "sudo cp /bin/bash ${bin_path}/"
    
    cat << EOF | sudo chroot ${root_path}
    grub-install --target=x86_64-efi /dev/sda --force --recheck --efi-directory=/boot/efi 
    update-grub2 /dev/sda   
    exit 0
EOF
}

create_fstab() {
    UUID1=$(sudo blkid | grep '^/dev/sda1' | awk -F 'UUID="' '{print $2}' | awk -F '"' '{print $1}')
    UUID2=$(sudo blkid | grep '^/dev/sda2' | awk -F 'UUID="' '{print $2}' | awk -F '"' '{print $1}')
    UUID3=$(sudo blkid | grep '^/dev/sda3' | awk -F 'UUID="' '{print $2}' | awk -F '"' '{print $1}')
    
    devName="\/dev\/sda1"
    UUIDStr="UUID=$UUID1\t"
    sed -i "/${devName}/ s/^/${UUIDStr}/"  /mnt/etc/fstab
    
    devName="\/dev\/sda2"
    UUIDStr="UUID=$UUID2\t"
    sed -i "/${devName}/ s/^/${UUIDStr}/"  /mnt/etc/fstab
    
    devName="\/dev\/sda3"
    UUIDStr="UUID=$UUID3\t"
    sed -i "/${devName}/ s/^/${UUIDStr}/"  /mnt/etc/fstab
}

partition_format_mount() {
    sudo /sbin/parted ${hdstr} <<EOT 1>/dev/null 2>/dev/null || exit 1
    rm 1
    rm 2
    rm 3
    rm 4
    mkpart primary fat32 1MiB 200MiB
    set 1 esp on
    mkpart primary ext4 200MiB 8200MiB
    mkpart primary ext4 8200MiB 100%
    quit
EOT
    echo ""

    execute_command "sudo partx ${hdstr} 1>/dev/null"
    execute_command "sudo /sbin/mkfs.fat -F32 ${hdstr1} 1>/dev/null"
    execute_command "sudo /sbin/mkfs.ext4 ${hdstr2} 1>/dev/null"
    execute_command "sudo /sbin/mkfs.ext4 ${hdstr3} 1>/dev/null"
    
    execute_command "sudo mkdir -p ${root_path}"
    execute_command "sudo mount ${hdstr3} ${root_path} 1>/dev/null"
    execute_command "sudo mkdir ${boot_path} -p"
    execute_command "sudo mount ${hdstr2} ${boot_path} 1>/dev/null"
    execute_command "sudo mkdir ${efi_path} -p"
    execute_command "sudo mount ${hdstr1} ${efi_path} 1>/dev/null"
}

install_os(){
    execute_command "sudo mkdir -p ${grub_path}"
    execute_command "sudo cp ${current_path}/grub.cfg ${grub_path}/grub.cfg"


    execute_command "sudo cp ${current_path}/x86_64-efi  /usr/lib/grub/  -raf"
    execute_command "sudo cp \"${current_path}/bzImage\" ${root_path}"
    execute_command "sudo cp \"${current_path}/initrd\" ${root_path}"
    execute_command "sudo cp \"${current_path}/rootfs.tar.gz\" ${root_path}"
    cd ${root_path}
    execute_command "sudo tar -vxf rootfs.tar.gz"
    execute_command "echo \"y\" | sudo rm rootfs.tar.gz"
     
    change_root
    create_fstab
    sudo grub-install --target=x86_64-efi  /dev/sda --force --recheck --efi-directory=/boot/efi
    sudo update-grub2 /dev/sda
    execute_command "sync" 
}

mainFunc(){
    copy_tool
    partition_format_mount
    install_os    
}

mainFunc

replay oldfred: