What was the purpose of equipping stabschwarms and staffels of StGs with Bf-110s and Fw-189s?

[Graham Boak]

Perhaps, but also as hack aircraft, used for liaison work. An Fw189 might do for hopping over to a nearby airfield/headquarters, or for picking up a shot-down crew from a forward field, or just for staff memebers to keep their hand in. A Bf110 could be used for more distant trips.

[Dénes Bernád]

Originally Posted by Graham Boak

Perhaps, but also as hack aircraft, used for liaison work. An Fw189 might do for hopping over to a nearby airfield/headquarters, or for picking up a shot-down crew from a forward field, or just for staff memebers to keep their hand in. A Bf110 could be used for more distant trips.

I'd say it was rather the other way around (without actually checking the aircraft types' ranges).
The Fw 189 was used by several high ranking Lw officers as transport.