I found this misleading on first read; I thought that the snapshot gets stored in $HOME/snap/<snap-name> and /var/snap/<snap-name> instead of the data that gets snapshoted.
Maybe a sentence like this will make this clearer:
A snapshot of the data that can be found in $HOME/snap/<snap-name> and /var/snap/<snap-name> will be stored in /var/lib/snapd/snapshots/ (see Data locations for more details).