The Prefect server that one can host themselves, after installing Prefect with the Python SDK client, is not specifically described as stateless within the provided documentation excerpt. The Prefect server is an API server backed by a database and has a UI for interaction. It serves as a counterpart to Prefect Cloud, sharing some common features. However, the documentation does not explicitly mention statelessness as a characteristic of the server. Generally, statelessness refers to an architecture where the server does not store any state about the client session on the server side.
If you want more in-depth information on the architecture regarding the state of the Prefect server, you might consider checking more detailed technical resources or documentation.