You are right. The Fed has to manipulate and play games since they do not do money. There are no USD involved in what the Fed does anymore. There was a time when settlements were done in physical cash where they could affect things directly. This is no longer the case.
So their operations are nothing more than expectations of what is happening. The Fed front runs everything in an effort to get the markets to buy in.
Fed purchases bonds
They actually put out swap arrangements which is technically purchasing (with an agreed upon sale) but they are not buying with USD like you or I would.
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Interesting. This is the key point.