Here's the script, should it be of benefit to someone, even if it of course needs to be modified:

    #!/bin/sh
    success=false
    teardown() {
      umount /mnt/backup/var/lib/docker || true
      umount /mnt/backup/root/.cache || true
      umount /mnt/backup/ || true
      for lv in root docker-data; do
        lvremove --yes /dev/hass-vg/$lv-snapshot || true
      done
    
      if [ "$1" != "no-exit" ]; then
        $success
        exit $?
      fi
    }
    
    set -x
    set -e
    teardown no-exit
    trap teardown EXIT
    for lv in root docker-data; do
      lvcreate --snapshot -L 1G -n $lv-snapshot /dev/hass-vg/$lv
    done
    
    mount /dev/hass-vg/root-snapshot /mnt/backup
    mount /dev/hass-vg/docker-data-snapshot /mnt/backup/var/lib/docker
    mount /root/.cache /mnt/backup/root/.cache -o bind
    
    chroot /mnt/backup kopia --config-file="/root/.config/kopia/repository.config" --log-dir="/root/.cache/kopia" snap create / /var/lib/docker
    kopia --config-file="/root/.config/kopia/repository.config" --log-dir="/root/.cache/kopia" snap create /boot /boot/efi
    success=true