You can use nsenter utility to “enter” a preserved mount and explore the file system as seen from that mount table. In particular you will find that /var/snap is, most likely, still mounted there.
This is a deeper question. Historically this would allow the application to see continuity in its /tmp directory. As things evolved the way /tmp is handled by snap applications, made it so that you can freely discard the mount namespace and applications would still see the same files in /tmp as they did before.
At a recent meetup we discussed removing the mount namespace persistence layer, mainly because it is highly complex and involves state (persistence means is is stateful) which has gone awry in the past. Removing persistence would cause some delay for each snap startup, as applications would no longer benefit from the caching. Some specialised applications would also change semantics as they grew to depend on the persistent mount table for correctness. Amongst this is, most notably, LXD, which uses another layer of mount table complexity on top of snapd.
I don’t believe we have a way to remove persistence today but I would like to see how we can support running fsck on /var/snap correctly. I will perform a small experiment and return to this thread with additional information.