Currently there are 2 native SuperZoom lenses for Sony A7 III and all of these lenses are autofocus (AF) type.
A7 III also has a sensor based image stabilization system which means that all of these lenses will be stabilized when used on A7 III.
Since Sony A7 III has environmental sealings (Weather Sealing), you may like to couple your camera with one of these 2 SuperZoom lenses with Weather Sealings.