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I've never read the three body problem (started it but just couldn't finish...it was very slow paced and there were moments when the Chinese...I don't want to call it propaganda but more like promotion...took me out of it, like the supposedly international coalition of scientists where the non Chinese ones were just cardboard cutouts) but I can speak to this:
Relativistic missiles. Nothing moves faster than the speed of light. So if you can get a big rock to go 95% of the speed of light, we'd only be able to detect that it's coming right as it hits. Sure, you can calculate the origin of the missile after it obliterates its target, but it's almost impossible to form a counterattack especially if the attacker just yoinked an asteroid from a different star system than their own and strapped an engine on it. And ESPECIALLY if your civilization is still mostly planetbound.
And a rock moving at some appreciable fraction of the speed of light could obliterate the Earth.
This is a very common answer to "how", but it comes with lots of problems in the Dark Forest context.
Absolutely not guaranteed to be the case. Earth's civilization could have easily had offworld colonies by now if circumstances had been slightly different, so a Fermi paradox solution that requires reliably blowing up Earthlike civilizations before they can get offworld doesn't work. They're already too late.
As I said previously, Earth has been quite obviously life-bearing for at least 2 billion years. Why wait until something like an RKV is needed, and even that is not guaranteed? They could have destroyed life on Earth far easier, and thus far more stealthily, if they'd done it a billion years ago.
I agree, either we've escaped detection or the dark forest theory is wrong.
Couldn't antimatter bursts get an object to extremely high speeds relatively cheaply?
Well, "relatively cheaply" is a hard standard to nail down. I would say "no", though. Antimatter is very expensive to manufacture and store and you're going to need a lot of it. All of the energy that comes out of an RKV hitting its target has to be put into it in the first place, probably several times over given the inefficiencies likely inherent in the process.
Fair enough, guess it depends on how many resources they're willing to sink into first strike capability. Maybe a strongly expansionist civilization would have such a more efficient use of resources it would quickly catch up to a dark forest predator trying to wipe them out. Like a swarm of piranha eating a shark.