I would think that at the speed of light, you would still be able to see light sources from outside the craft. Light sources that you are traveling towards would be compressed into brighter sources. Light sources that you are traveling away from would be a split second of an image as you travel as fast as the light you are viewing. It would never change.
Yes, as one becomes more and more relativistic, strange appearances take place. As you said, what is ahead gets squeezed toward the center, thus increasing that central brightness. The blueshift will also affect the brightness. But the biggest effect, I think, will be the brightening due to the increase in the photon flux - the faster one travels the more photons per unit time one encounters.
Imagine all those photons coming from, say, Rigel. If you could travel there in minutes you would encounter all those hundreds of years of photons of that stream.
What may appear even stranger is what happens in the rear view mirror. The rear view will see everything expand and become more and more red, and more faint, the closer one nears light speed. I’ve read of yet more oddities for other window views, especially side views, but I’m unclear on them.