Entangled with is a better way to think about it. The Fed strongly influences the rate curve. But the rate curve also influences the Fed. And trading rates isn't just about predicting what the Fed will do (though that's a big piece of it).
How much does Fed actually consider the shape of the yield curve? Powell's recent comments indicated they focus on front of curve, as opposed to something like 2s10s. Aren't central banks like ECB/BoJ more attentive to overall shape?
Quite a bit. The February MPR cites "yields...across maturities" in the first sentence under financial conditions [1]. (One of the entire novelties of OG QE was the purchase of longer-dated securities.)
[1] https://www.federalreserve.gov/monetarypolicy/2022-02-mpr-su...