Embeddable Studio - Upload an image via config?

Try this instead. ControlType was deprecated with the introduction of Property Templates in 11. Additionally, the Url property template supports options to enable local (uploading) or remote (linking) and inline previewing within the configuration UI. More in the url Template.

<propertyGroup id="options" labelText="Options">
  <property id="backgroundImage" labelText="Image" dataType="Url" validExtensions="gif,jpg,jpeg,png"  allowLocal="true" allowRemote="false" enablePreview="true" />
</propertyGroup>

Thanks Michael, that worked.  This being said, if we have custom widgets that use the old ControlType functionality...I'm assuming we'll need to update those to this syntax when we upgrade?

All documented legacy property types are still supported with automatic mapping (via the IPropertyTemplateAdjustment)  to resolve to the new IPropertyTemplate -based versions. As for why your particular case didn't work, it unfortunately was not a publicly documented control type. While it would be possible to implement your own IPropertyTemplateAdjustment for this type, it would be better to just switch it to Url. 

Also, here's the complete list of supported Property Templates. They'll handle all previously-supported legacy ControlTypes along with lots of new scenarios, both flexible and generic and highly specific.