I would be more concerned about writes going through additional fs layers and about abrupt termination of a container.
You generally are trusting a database to keep your data safe, so those things will contribute to data loss.
Remember the freakout about PostgreSQL not handling sync() correctly on Linux due to ambiguity in the man page? Having a networked filesystem + additional abstractions (like layers) etc only reduces data durability.
Except you never do that (having your DB directory be in the container rootfs). Nobody does, because then (beside the performance/reliability impact you mention) if the container goes (docker rm) the data goes. You're always gonna use a Volume for this kind of cases, be it K8s volume or Docker volume, and these, as neighbour message mentions, are just bind mounts (or actual mounts in certain cases), so no layers, no overlay, nothing of the sort.
You generally are trusting a database to keep your data safe, so those things will contribute to data loss.
Remember the freakout about PostgreSQL not handling sync() correctly on Linux due to ambiguity in the man page? Having a networked filesystem + additional abstractions (like layers) etc only reduces data durability.