The type of restoration you are trying to do will work much better if you use the Grub bootloader instead of systemd-boot, because you will be able to store your kernels and initramfs images on a Btrfs partition and include them in your snapshots. The choice between these bootloaders is presented in the installer, so you could just reinstall and choose Grub this time.
Or, you can try your luck switching bootloaders on the installation you have as was done in this thread: