More spoilers below:

They actualy did a fair amount of geopolitical manipulations. That formed most of the plot.

In the end, it turned out to be MAD that saved us, but setting up the MAD scenario involved secrecy from them (or else they would have stopped us before we could trigger it), and from the rest of humanity (because an official plan to destroy Earth would never have been approved).

It seems like the manipulations were exceedingly silly. It seems like having the sophont start a nuclear war would be straightforward. It was hard for me to suspend disbelief in the sense that it had planet-sized computational power and the ability to manipulate some information on the subatomic level, but couldn't find a vulnerability in aging nuclear launch protocols? The history of near misses with human controlled nuclear weapons suggests a variety of vulnerabilities exist that wouldn't require e.g. directly hacking into command and control. Could it spoof images/data to a sub? Could it cause hallucinations in a large sensor array that feeds data to Norad or a Chinese/Russian equivalent?

Re MAD: I think a plan to destroy Earth would have been easily approved - much like it was in 1960-now, with ICBM and SSBN retaliatory strike capability. Obviously somewhat different in that those MAD-based nuclear wars would be extinctive but not deny the planet to the trisolarians, but the idea that human governments aren't ready to commit to that seems wrong given our history.

The aliens specifically wanted Earth because of its life. A nuclear war would damage the planet's ecosystem too much.

> In the end, it turned out to be MAD that saved us

Read the rest of the series and this answer gets more interesting. I will not say any more about the outcome (spoilers)

They cared about our stable single sun more than planets. We were not on the level to destroy our sun, or the planets themselves