That's ignoring the global nature of the supply chain. If supply is constrained and you give money to your own people, they may bid up prices some, but not by the entire amount because mostly what they're doing is using the money to outbid people in other countries. Which also means your people get more of the stuff.

This cancels out if everybody does it, but not everybody can do it.

The increase in demand from people having more money may also make it economical to increase supply faster and alleviate the shortfall sooner.

Exactly right.

Demand was induced with money printing. Supply was restricted with lockdowns. When demand outstrips supply, prices rise.

More money supply likely accounts for some increase in demand. But the lockdowns themselves likely had more effect on demand than more cash. People need or want more things when they travel less and have fewer services to consume. When behavior changes in large ways, demand shifts to different things. Printing more cash didn't drive demand for n95 masks. It also didn't drive demand for things like flour and many other commodities. With the exception of those in extreme poverty, most people didn't run out and buy more toilet paper and flour because they got a stimulus check.