Also, knowing a bit of orbital mechanics really screws up the whole concept of the Trisolarans. There are so much easier solutions to their problem than staging an interstellar invasion.

For example, the only way you can have three stars orbiting each other without one being ejected is to have them arranged how the Alpha Centauri system is arranged. Here, two approximately Sun-mass stars orbit each other at about the same distance as Neptune orbits the Sun. Then there's a distant red dwarf that is a quarter of a lightyear out in a wide orbit, orbiting both of the larger stars in common. You can't have three stars orbiting each other all at a similar distance. One will inevitably get ejected or collide with the others very quickly.

It's entirely possible for planets to exist in such a system. We've found planets around at least one of the larger stars in Alpha Centauri. Now, if you have two Sun like stars orbiting much closer, like Earth-Sun distance, it wouldn't be possible to have a stable planet in the habitable zone of either star, or in a habitable orbit around both stars. So there are arrangements where no habitable planet can stably exist, either orbiting one or both.

But as you note, nothing could evolve on a planet that isn't reasonably stable over billions of years.

But even if you ignore that, there are so many better solutions to the Trisolan's problem that trying to invade Sol. For example, you can almost always find a stable orbit really close to just one of the larger stars. They could build large space habitats really close to one star, closer than the distance of Mercury. And then they can simply use solar shields and mirrors to keep those habitats at comfortable temperatures. And the same works in reverse. Have two large stars orbiting really close, closer than the orbit of Mercury? Maybe there isn't a stable orbit between them. Instead build artificial habitats distant from both of them, like at the orbital distance of Neptune. Then just rely on large mirror arrays to concentrate the dilute sunlight at that distance. Or hell, just skip the mirrors and use reactors to power your habitats.

The point is, by the time you become a real space-fairing species, capable of getting into space in a big way? The "habitable zone" around a star completely loses all meaning. If we had good access to space, here in our solar system, we could build orbital habitats anywhere from a fraction of Mercury's distance from the Sun to well outside the orbit of Pluto. You just need to use the right combination of mirrors to either diffuse or concentrate solar radiation towards or away from your habitats. If you have space flight, you don't need a stable planet in your system's habitable zone. You can just build entirely artificial habitats in whatever orbits your system does have that are reasonably stable. And they don't even have to be perfectly stable, as you can use those same mirrors as solar sails to correct for any slight gravitational perturbations. Doing this is absolutely orders of magnitude easier than trying an interstellar invasion. And in the Dark Forest context, it's a lot less likely to get your civilization noticed by some hungry predator species hiding in the dark. The engines of your giant space armada are likely to be visible at interstellar distances.