Usually employment is good when inflation is high, and when Fed kills inflation it will kill employment too. I think it's called Phillips curve or something.
One way to think of this is by splitting the economy into companies that make consumer goods, and those that make capital goods. For example, think of airlines, and Boeing.
When interest rates go up, airlines become more reluctant to buy new planes. The airlines may still have full seats, but things slow down at Boeing. Maybe they lay people off.
Capital goods companies are something like 40% of the economy. Higher interest rates hit them harder than they hit consumer goods companies. The layoffs often start there.
I think that's the mechanism (or at least part of it) where higher interest rates lead to unemployment and recession.
