Agree that it is something like a JST connector. Relatively generic and widely available.
However, a CRITICAL detail is the PITCH of the pins.
EXACTLY what is the space between the pins?
1mm? 1.27mm? 2mm?, 2.54mm? etc.
Also, that keyway may indicate a custom connector.
You may have to take the standard JST mating connector and file a groove for that key.