Kubernetes distributed filesystem
You can use a Hadoop Compatible FileSystem such as Ceph or Minio. Both of which offer S3-compatible REST APIs for reading and writing. In Kubernetes, Ceph can be deployed using the Rook project.
But overall, running HDFS in Kubernetes would require stateful services like the NameNode, and DataNodes with proper affinity and network rules in place. The Hadoop Ozone project is a realization that object storage is more common for microservice workloads than HDFS block storage as reasonably trying to analyze PB of data using distributed microservices wasn't feasible. (I'm only speculating)
The alternative is to use Docker support in Hadoop & YARN 3.x