Proposal

In order to better correlate Prometheus and OpenTelemetry metrics, we would like adopt the OpenTelemetry naming specifications (link) on Prometheus metrics.
This requires to discover the name of the deployment/cronjob/job that create pods so in addition to supporting __meta_kubernetes_pod_name in kubernetes_sd_config, we would like to have __meta_kubernetes_deployment_name, __meta_kubernetes_conjob_name, and __meta_kubernetes_job_name.
This feature seems to be implemented in the OpenTelemetry Collector K8s Attributes Processor navigating from the pod description to the controlling daemonset/statefulset/replicaset and again navigating to the controlling deployment/cronjob/job.

For feature parity with Openelemetry, the Prometheus discovery could also add support for discovering the daemonset/statefulset/replicaset.