Why did the trisolarians gave up so easily, if they had the technology and knowledge to save the solar system?

I just realized something that doesn’t really make that much sense.

Trisolarians gave up on the solar system the moment Gravity transmitted the coordinates. At first, this made sense - the solar system was doomed to death. However…

The discussion with Luo Ji when all this happened reveals that the San-Ti knew the “sign” of innocuousness, and they knew Trisolaris is branded with the sigil of danger - the slow bubble their second fleet left. Tianming’s story later makes it obvious that they knew all about curvature drive, its effect on spacetime and the speed of light, and the slow fog, the sign of innocence.

Trisolaians had the knowledge, the technology and frankly a huge ass motivation to do so. Why not? Why give up so easily on a planet that seems paradise to them, if the alternative is an uncertain survival in deep space without a certain destination? Even if they reject the idea of constraining their entire civilization to a single star forever, they can always split the fleet, and send only a part of it to Earth.