Normally I don't answer my own questions, and certainly not right-away, but since there are forces trying to close the question in part because the answer will not be about space exploration, I'd like to get at least one answer in, and at the same time demonstrate that they are wrong.
Will Kerbal Space Program 2 have Lagrange points, halo orbits, and other 3-body goodies?
It's pretty clear that the answer is "nothing in the current information presented by the OP suggests that this is the case." It's also taken to be self-evident that three-body calculations are way, way more complex for the game to simulate, and for the user to try to understand and take advantage of. But further discussion of that is outside the scope of the question as asked.
Let's start from the official page for KSP-2:
Next-gen tech, colonies, and systematic resource gathering all lead to a whole new level of exploration: interstellar travel. In Kerbal Space Program 2, these interstellar technologies pave the way to a host of new celestial bodies, each comprising new challenges and harboring new secret treasures. Among them: Ovin, a ringed super-Earth with relentless gravity; Rask and Rusk, a binary pair locked in a dance of death; and many more to reward exploration.
Rask and Rusk's "Dance of Death"
The questions Why can't supermassive black holes merge? (or can they?) and Which things “LIGO can see things that LISA can't”, and vice-versa? both link to CNET's Astronomers discover two ferociously fast stars locked in a death spiral. Death spirals or "dances of death" refer to a pair of stars that orbit so close that tidal forces will slowly rob them of orbital energy, causing a slow but inevitable path to a merger, often with spectacular consequences. On the scale of KSP gameplay time though, they would appear in a close but stable orbit.
Binary star system and 3-body problem
That the pair is mentioned so prominently on the website as evidence of interstellar travel, it's pretty clear they are saying that you'll be able to visit this binary star system. If not, what would be the point of putting a binary system in the game that you can not visit?
However, one would likely visit a planet orbiting around the intimate, death-defying binary pair of stars, not the stars themselves! As discussed in this answer to periodic inclination change circumbinary planet the pair would rotate around each other much more rapidly than the planet would orbit them. The primary gravitational perturbation effect on orbits near the orbital radius of the planet would be more like a super-strong J2, as if the pair were a super-oblate star. Unless you were navigating close to the pair, you would not need a full-blown 3-body solver to approximate your trajectory.
So to the OP's suggestion that
It seems that navigating anywhere near a binary pair of anything would require some 3-body physics...
the answer is technically yes, but when playing KSP you would not be "navigating anywhere near a binary pair" of stars, and per the website, it is a pair of stars, not a pair of planets.
Based on all of the material presented in the question and in the KSP-2 website, currently there is no evidence that any "3-body goodies" will be present. Further releases may share more information, but currently nothing points to this happening.