Let's say I have a goal of running a marathon, so I decide to start jogging every day. Is my daily jogging a side-effect of my goal to run a marathon? I wouldn't say so. Rather, jogging every day is an explicit course I've set out on with the hopes of achieving my main goal. Daily jogging is a sub-goal of the main goal, if you will. This logic can be applied to the Fed. The main goal is to lower inflation, and the chosen course of action (i.e. the sub goals) are to lower economic growth and to increase unemployment.
A side-effect would be something akin to knee pain. I can't jog without hurting my knees, but having pain in my knees isn't something I explicitly set out to do.
A side-effect of Fed policy would be something like the gilt crises in the UK. Higher US rates increase yields on UK bonds indirectly. But that isn't something the Fed is actively setting out to do.
You can't run a marathon without your daily jogs. Inflation can be lowered without spiking unemployment. It's unlikely. Hence the Fed's messaging. But until recently the Fed forecasted a soft landing, i.e. growth and low unemployment amidst rising rates and falling inflation.
Better analogy: engine temperature. You're driving and keeping an eye on the thermometer. You see the temperature is low and so feel comfortable accelerating. The goal is getting to your destination faster. The low temperature lets you accelerate, which in turn raises the temperature. But raising the engine temperature wasn't the point. It reverses cause and effect to say your goal was to raise engine temperature. It wasn't. Engine temperature was simply a limiting factor you were paying attention to.
The relationship is sufficiently complex to permit e.g. falling unemployment, falling (not negative) wage growth, falling (including negative) growth and falling inflation. It's not a deterministic system.
> in a sense increase combustion is a goal
No, it's not, because the goal--reaching the destination quickly--would be accomplished equally well in an electric car with no combustion. That's the difference between a goal and an effect.
I think you’re falling for the no true Scotsman fallacy. We started this conversation talking about whether or not the Fed’s goal is higher unemployment. I presented an argument, in the Fed’s own words, that they plan on lowering inflation by weakening the labor pool. And your response is “that’s not really a goal.” I disagree and, and I don’t see a productive way forward for this conversation. At the very least, you should accept that this is a valid interpretation of the Fed’s own words, and not just some conspiracy theory being peddled.