A bit of fine-tuning:
Assuming the star is like Sol, we'd be the best off if we speculated that Veridian III was only about five lightminutes distant from it - because only then would Veridian IV, another known Class M world, still also fit inside the "life belt" of the star.
As for the death scene of the star reaching the planet that fast, perhaps it did not? Perhaps the star continued burning normally for the next five minutes, as far as Picard and Soran could tell - but a great "shadow" of some sort expanded from the detonation at FTL speed, making everything look dimmer?
After all, the darkness was achieved by the time-honored movie trick of "nuit américaine", shooting in bright daylight but playing with the white balance (or, previously, using a different quality of film, intended to be compatible with studio lighting rather than sunlight). That means that not only does the big source of light on the sky grow dim, but any light moving between surface locations, say, being reflected from or emitted by the equipment we see, is also unnaturally dim. This would be more consistent with a "dimming field" than with the loss of sunlight.