I don't see why China would fund such purchases through ad hoc currency printing as opposed to normal budgetary avenues, but regardless why would it matter?

The Chinese government possesses enormous purchasing power ultimately because there is such high demand for Chinese goods.

If the paper currency for which you have some unexplained contempt were the key to China's purchasing power then countries like Vietnam or Somalia or Croatia would have exactly the same ability.

A Somali gets a briefcase filled with Somali cash and starts buying up US properties willy-nilly, right?

No. Because nobody wants Somali cash because Somalia does not produce anything that US purchasers want to buy.

It seems to me what you are doing here is connecting China making strategic purchases through proxies (sounds true to me) to Chinese currency manipulation (also sounds true but completely unlike what you are describing, it actually reduces Chinese purchasing power).