So..... If you were in your car, traveling through space at near the speed of light, the stars you look at through your windshield would be twice as bright as you bear down on them.
While the stars in your rear view mirror would barely be visible because you're out running their light.
No. Not exactly.
First, the brightness has nothing to do, directly, with the velocity of the star.
The velocity of the star, relative to the observer, red-shifts (going away from you) or blue shifts (coming towards you) the light that you, the observer, see from that moving object.
Now, blue light is brighter (more energetic) and at high relativistic speeds, there can be some relativistic “beaming”, or apparent amplification of luminosity by a jet of energetic (light emitting) matter coming at the observer. We see this in astronomy - it’s measurable. There are objects in the universe that emit matter at very high speeds, and it is blue-shifted and more luminous than it would be if it were going slower.
But…in your relativistic car, you’re not “outrunning” their light - because, for you, at near the speed of light, time has slowed. So, what you see is the light coming at you from both sources at, well, the speed of light, though with significant blue and red shift.
There are several difficult, but important, concepts when discussing special relativity.
The first is that there is no absolute velocity, only velocities relative to you, the observer.
The next is that the perceived speed of light is a constant, C.
The next is that you can never get to the speed of light itself, only close. If you look at the equations, when V=C, the terms for M (mass) go to infinity, so, best case, you’re getting to 99%, not 100%.
The next is that the faster you go, the more that time dilates so that you still see light coming at you at C.