You can find the MLflow version in the runtime release notes, along with a list of every other library provided. E.g., for DBR 8.3 ML, you can look at the release notes for AWS, Azure, or GCP.

The MLflow client API (i.e., the API provided by installing `mlflow` from PyPi) is the same in Databricks as in open-source. The managed MLflow Tracking Server and Model Registry are different: those are integrated into Databricks' scalability, security and access controls, and UI.