In general WSL can not really run services, be it through systemd or any other init system, as WSL does not run any init system.
Some WSL aware programs (like docker) install itself into separate WSL machines and then start a hidden session. They basically do what rudolfb describes.
Postgres is not WSL aware, but you can install postgres on windows and connect to it from your in-WSL application (WSL is transparently bridged to the hostnetwork).
