I ask again, why would a viewscreen reflect bridge lights?
Unless it where a window made of extra stong glass that turns into a viewscreen when needed. IE, a non-reflective one.
It makes sense, and would look cooler in the film anyway.
A viewer that defaults to a window simulation may have reflective glass for aesthetic purposes.
It looks like the viewer/window is viewed from a place slightly to the left of the centerline of the Bridge set, and yet the view of the outside is as if the camera is looking leftwards from a place to the right, and perhaps too far forward (or too far to the right) to see the USS ENTERPRISE decal on the saucer.
You can clearly see the "-" in the NCC-1701 running through the centerline of the saucer, to the right hand of the view, with the centerline dividing the port and starboard sides of the bridge tracing aftwards to the left from the bow lip of the saucer, where it would presumably intercept the bottom of the Bridge module to the right.
If this is actually a Window, then we would get a fixed view forward directly over the centerline of the primary hull.
In addition, the black openings on the bottom of the Bridge module facing Port and Starboard would be reflected in the layout of the Bridge interior set.
Also, looking at a different view, the shape (Width/Height) of the visual portal in question does not match between interior and exterior.
A window would be an interesting design feature, but the presumption that it is a window simply does not hold water under close scrutiny.