[superposeur]

If you travel through a localized clump of stars then yes, as you describe, the clump would be pancake-shaped. However, the Lorentz transform of an infinite lattice is another infinite lattice, just one in which the spacing between stars in one of the three directions is smaller. So, in particular, the average density everywhere remains uniform (no matter where you are situated within the lattice).

The reason you don’t see an isotropic distribution of light from this uniform density is the distortion due to aberration + the synchrotron effect you mention (which makes the stars in the forward direction brighter).

So, in conclusion no “critical angle” but the dots of light appear more densely concentrated toward front and they are brighter, bluer.