Currenty, when switching from one scene to another, the mode
of the active objects (before & after) is left untouched.
This becomes a workflow problem when trying to work across
different scenes. E.g. when opening the new "Storyboarding"
template and scrubbing to the next scene strip, the Grease Pencil
object is now in Object Mode, when in the previous shot it was
in Draw Mode.
To solve this, when syncing scenes try to change the mode of
the next active object to the mode of the previous active object
if the type of the object is the same.
Pull Request: https://projects.blender.org/blender/blender/pulls/146981