Hello, you need to use <pacman> if you do it inside the root of current system or <pacstrap> if you install something on the external root.
Installation of various kernels does not differ. The <pacman> activates the trigger to rebuild initramfs (initial ram file system) and update the configuration of GRUB. But you can do it manually too, and do it inside root if you are install the kernel using the <pacstrap>

Thank you for your answer and desire to help. I realized that I can pacstrap for example:

 # pacstrap /mnt linux-libre-hardened 

I want to understand what I need to do next since I can't use the same command as when installing Linux-libre-lts

 # mkinitcpio -p linux-libre-lts

My mistake, I wrote the kernel names incorrectly!

Everything works correctly!

# pacstrap /mnt linux-libre-hardened

  # genfstab -U -p /mnt >> /mnt/etc/fstab

   # arch-chroot  /mnt

   # nano /etc/mkinitcpio.conf

MODULES=(i915)
HOOKS=(base udev autodetect microcode modconf kms keyboard keymap block encrypt lvm2 filesystems fsck shutdown)

# mkinitcpio -p linux-libre-hardened

The only problem was a warning about the absence of the isci module and I also could not compile the kernel with hooks consolefont

I also don’t understand, if for example I want to change the kernel to Linux-Libre-Lts, I install Linux-Libre-Lts and remove Linux-Libre-Hardened, will everything work correctly?

i would not uninstall linux-libre-lts - multiple kernels may be installed together; and they will all work - i recommend that you keep two or more kernels installed at all times

Hello Bill . Thank you for the useful recommendation.