I updated to gnome 47 , I can't login to either the wayland or the X11 session

[BluishHumility]

You will have to manually edit /boot/grub/grub.cfg so it points to your actual installation instead of a snapshot. This old thread is a similar case:

Can't restore snapshot

You need to manually edit /boot/grub/grub.cfg and find the boot entry for your install. When did you do that? You may have already been booting off a timeshift snapshot. That doesn’t change your existing snapshots. It means that new snapshots will come from snapper.