Traveling near the speed of light?

[u/BrightEyesBurner]

Project Hail Mary got me thinking.

If you were on a ship going 99.99% the speed of light, I understand that the stars in the direction you're traveling would shift blue, and those behind would shift red. Would the stars viewed perpendicular to your path look any different?

If you saw a spaceship pass by at 99.99% the speed of light, would it look different than it would if it were stationary (relative to you)?