Elasticsearch requires the filesystem to act as if it were backed by a local disk, but this means that it will work correctly on properly-configured remote block devices (e.g. a SAN) and remote filesystems (e.g. NFS) as long as the remote storage behaves no differently from local storage.
Local SSDs are always recommended, which may not be an option in a k8s environment, but other types of storage are often used. It is usually fine as long as the guidance in the docs I linked to are followed.
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