Postgresql is the internal database used by the Delphix Engine to store configuration metadata.
Pichat is not installed, but you may have seen it come up as a false positive in a network scan. Pichat uses TCP port 9009 and this port is registered with IANA as the official pichat port. On a Delphix Engine, the java process that we refer to as the management stack has a listener on TCP port 9009 for internal use, but it is
not a pichat server.