There are great threads in there. The dark forest as an illustration of paranoia matches up with the culture of fear in unstable political climates, and is also a hopeful description of peace in a nuclear time. "Hot contact" with an advanced alien race mirrors the US and China. The exploration of hidden information with sophons, wallfacers, and star signaling.
Foundation was written when the US was cementing its empire. It thinks about legacy, decline and planning. The series reads as safe, cozy, paternal (some of the main antagonists are petty bureaucrats and gentle public disapproval).
Three Body is much more chaotic, jumbled, in the trenches. The systems are bigger and stronger than the people, practically and narratively. Asimov's robots were essentially human, dealing with how to be good citizens. It's all human scale. Liu's people are triggers for events far larger than themselves.