Quantitative easing increases the money supply. They've injected trillions. Who got it is a separate question.
[0] https://positivemoney.org/how-money-works/advanced/how-quant...
If banks would buy financial assets and create money in the process as described in the post, then that would certainly be inflationary. (e.g. I can imagine hypothetical legislation that forces banks to buy government bonds, that would be the time to run for inflation protection.) As far as I understand, this has not happened, or at least not to the degree that it caused inflation. The effect of QE has been to increase bank reserves but not the money supply, which is why we haven't seen inflation since the financial crisis.
I can't find a source that explains the mechanism for how QE affects the economy.
[0] https://www.investopedia.com/articles/investing/051315/what-... [1] https://en.wikipedia.org/wiki/Deflation#Deflationary_spiral
When the central bank later buys those bonds from banks (they never buy them directly), something different happens: the bonds are exchanged for "bank reserves", a different type of digital money that only exists as numbers in the central bank's database. This "money" cannot be used to buy groceries.