While supply chain problems were real during the pandemic, especially w.r.t. automobiles, QE is by far the driving force of our current economic situation. Here is some data to put your talking point into context.
Look at the recent production some of the items being severely impacted by inflation. Now look up their price charts (you can use February before Putin invaded Ukraine to eliminate another variable).
Wheat: https://www.statista.com/statistics/267268/production-of-whe...
Meats: https://www.statista.com/statistics/237632/production-of-mea...
Steel: https://www.statista.com/statistics/267264/world-crude-steel...
The only economically significant shortages (as defined by lower production) were in automobiles and oil: https://www.statista.com/statistics/262747/worldwide-automob...
You could argue that demand for oil was also lower, because of fewer automobiles and, of course, lockdowns. Crude oil prices were at 2018 levels until the very end of 2021 (when inflation was at 7%), so you can't blame inflation on that.
Did Covid affect productivity? Undeniably. A significant portion of the world population was literally locked down for months. Is that lower productivity and resulting supply chain disruptment a contributor to inflation? Probably. Although without any government intervention, prices probably would have depressed similar to the 1930's as the economy contracted and cash became more valuable as paper loans eliminated money generated by the money multiplier.
But these statements suggest a low level misunderstanding: "and very little (if any at all) has to do with QE" and "one of the world's largest oil producers started a war."
QE is a major contributor (hence why it is finally being rolled back to undo the damage...) and the inflation rate was 7.9% in February, BEFORE Putin invaded Ukraine. If I had to guess a significance, I'd say overall economic price increases are a consequence of 70% QE, 20% supply chain, 10% Russia. Another thing... look at the stock market. If the supply chain truly demolished the value of the economy, why did the market go on a historic bull run? Either the supply chain issues were not as bad as you think, or the Fed way over-quantitative-eased and disconnected prices from reality by expanding their balance sheet with literal securities, and of course the historically low interest rates.