This morning's launch of an ISS resupply mission by SpaceX happened in a beautifully clear sky just before dawn. As hoped, the not-yet-risen sun illuminated the entire flight path from just after launch to the eastern horizon.
The first stage was almost as usual, other than the last portion before separation being well illuminated. Additionally, the first stage was not returned, therefore no boost-back burn and it appeared to "tag along" with the second stage for most of the flight. That was great to see.
According to The Curious Droid's video, there's a two minute dissertation that states atmospheric pressure is a factor in engine nozzle bell shapes. As the rocket climbs, atmospheric pressure drops and the thrust becomes less efficient. More of the engine thrust is not parallel to the flight path and is "wasted."
In this photo, you can see the contrail from the first stage, well illuminated by the sun, but also the beginning of what appears to be the expansion of the exhaust gases due to higher altitude. I'm not sure where in the photo-timeline the first stage separated, but I believe that this is after the first stage separated.
In this image, the exhaust has expanded substantially. The camera did not capture all of the illuminated area, which would appear to the naked eye to be at least another fifty percent larger.
Certainly the approaching sunrise contributed to this effect, but is the flaring of the exhaust this immense?
If so, one would guess that it's simply not visible in lower light conditions or in full sunlight.