Is Inflation Inevitable with Market Interjection via the Fed?

This is my current understanding of the monetary system, someone please correct me if I'm missing something. I've been trying to wrap my head around this.

So lowering rates causes expansion of the money supply multiplier, which leads to a lower price elasticity of demand, which is then perceived as inflation.

And hiring rates leads to a contraction of the money multiplier, but creates government budget deficits due to the cost of servicing bonds at higher rates, which in turn creates more m2, which leads to inflation.

So it seems to me that market interjection via the Fed ALWAYS leads to inflation in the long run, and there doesn’t seem to be any way to tame it with our current system. Even raising rates basically creates new money. Am I missing something here?