It's literally the mandate of the Fed and the only levers they have are rate changes and threats of future rate changes.

Something something the measure becomes the means or something.

the economy runs itself, mostly. rates are one of the very few direct knobs anyone has that are sort of predictable.

well you can also commit fiscal suicide like the recent has-been-a-PM of UK showed, but in that case the economy runs you quite explicitly.

Their goal is to reduce inflation. Increasing unemployment, is a side effect of rate hikes but ultimately, reduces demand for consumer goods thus reducing inflation.

Inflation in staple supplies and food are radically inflated too and they aren’t reducing when people go on unemployment.

Their goal is to keep inflation steady at a manageable rate, and to prevent any deflation at all. Since inflation indicators haven't been too reliable in the last 20 years, they were caught horribly off guard. But ideally, they would make small changes one way or the other to maintain a nice equilibrium that would keep employment levels relatively stable.

True in the ideal case.

There are a ton of levers (not all under the Fed's purview). This is just how capitalism works though, others must suffer at the expense of capital. It's bad enough when the government doing the bare minimum, like trying to put a bunch of people to work to replace our crumbling infrastructure, gets decried as "socialism". Those voters must not understand (or simply not care) that voting for the same corporate interests over and over again will just lead to the working man sacrificing more to big business.