Yes, people are ignoring the second-order effects. Just because California can’t directly print money doesn’t mean they aren’t contributing to the macroeconomic factors leading to the Fed feeling the need to print more money.
Right. One way to combat inflation is to save money. The fed encourages this by increasing the interest rate. If california truly wanted to reduce inflation, it would simply retain those $1000 checks. Taking money out of supply reduces inflation.
California doesn't want to reduce inflation. (It would be of at least questionable legality, too. Because monetary policy lies with the federal government - Article 1, Section 8)
What California does want to do is ensure poorer people aren't bearing the load disproportionately.
Also, while we can certainly argue if this is the best use of those funds, a quick reminder that the size of the US money supply is almost 22 trillion. We're about $6T above 2019 levels. California retaining $10B is not going to have any measurable impact on inflation.