To nit pick I would assert that the price basket is more dependent on the actually supply demand constraints but when there is free floating supply to be utilized but demand cannot catch. Than lowering interest doesn't necessary cause an increase in costs i.e inflation but can actually ruin the other way for some goods. That's why despite inflation being rough the actual cost in value of TV is so far down the economy grew and can now cheaply satisfy that demand. I don't think this was a great argument because I didn't link fed actions to that growth.
A better negative example is though in the US a large issue in the 1970s we had Regan Stagflation was austerity weakened demand and the feds levers simply couldn't deal with that type of inflation. The fed cannot directly influence solving supply issues only direct investment does that
You're right that stagflation shows the Fed can’t fix supply shocks with interest rates alone, but calling it “Reagan stagflation” and blaming austerity doesn't quite pass muster to me. The 1970s mess was mostly caused by oil shocks and entrenched inflation. The Volcker rate hikes (and Reagan’s early years) were the painful cleanup, not the cause.
[1] https://en.wikipedia.org/wiki/1980s_oil_glut