I’m not sure if this is the problem, but it might be that cp -r creates the new files according to the current user’s umask and uid/gid. Which, if done from a live CD, would be a user that does not exist on the system when you try to boot it. What you want is cp -a.
https://unix.stackexchange.com/questions/44967/difference-between-cp-r-and-cp-a
You might be able to correct this without re-copying everything by using rsync. I don’t recall the incantation off-hand (you’ll want to google it) but I think you want rsync --partial --archive.
https://serverfault.com/questions/141773/what-is-archive-mode-in-rsync
Edit: Would also help to know if you are getting any error messages at boot time.
Yes to rsync. It will update the destination files in place without deleting the source files (unless you provide that flag – don’t.)
You might actually be screwed if you ended up overwriting the EFI variables in
/sys/firmware/efi/efivars. See https://unix.stackexchange.com/questions/414799/efi-variable-entries-in-sys-firmware-efi-efivars.If you still have all your files backed up, it might be easiest to reinstall the base system and then selectively copy back over the directories you want with
cp -a. Sorry to be the bearer of bad news, but if you can’t even attempt to boot, that’s not good.