Red- / Blueshifting and relativistic length contraction at $0.8c$ - How would it look?

Surprisingly, 0.8c is not really fast enough to do anything visually freaky! You need to go much closer to the speed of light (according to some observer or "scene").

What you actually see is rather more complicated than the "compressed" scenery in most pop-sci "explanations" (looking at you, Mr Tompkins!). It is described by a combination of Doppler Effect (red/blue shift), and relativistic beaming (brighter in front, darker behind), aberration (things you have gone past can appear to the side in front of you!). All these effects are derived from the Lorentz Transformation, but the transformation is not the whole story.

Anyhow, enough bluster, there are a few artifacts on the internet that can give you some idea:

This really old video

A Slower Speed of Light (unfortunately now abandonware)

My videos

Of course there are plenty of others, but you should now have enough pointers to look around for yourself!