The Fed’s response to this is to stymie economic activity, which will lead to layoffs and lower spending, and that will in turn reduce demand because people have less money to spend.

Doesn't the economic activity have to slow just because there is less stuff to buy? If fewer cars are available for sale, we will need fewer car-transfer drivers, car salesmen, and ad copy writers extolling the virtues of unobtainable vehicles. Interest rates don't do that. Supply shortages do that.

The only policy question is who will get the remaining supply of goodies. Inflation rations by bargaining power. The price goes up until people who cannot raise their price are priced out of the market. Raising interest rates also rations, but by a different dynamic. If the interest on my adjustable rate mortgage rises, then I have less left over to buy a TV, so demand for TVs is reduced by the rise in interest rates. The rate rise does slow the economy by raising the cost of capital, but the shortage was inevitably going to do that anyway. The policy move merely channels the slowdown, diverting it from the disruptive inflation channel (renegotiating the price of everything is a very resource-intensive process) to the less disruptive demand channel.

BTW, as a derivatives trader, you should be aware of the effect of commodities futures on price levels.