Confucius centers act more as a way for the CCP to keep tabs on their foreign students and "correct" them should they start straying from the official ideology or become politically active in a way that that runs counter to the parties interests. The spread of pro-china propoganda is simply an inception style front to hide their true purpose. Ostensibly they are for cultural exchange, but everyone knows it's for CCP propoganda, and since everyone knows that they don't work well as CCP propoganda, which means their true purpose is obviously something else.

What that is is to keep Chinese students from organizing politically abroad.

Buying land is different and it's simply economics as rich Chinese capitalists need a place to dump their money that is outside of CCP control. Can't buy land in China, can't trust Chinese banks.