i've already done this.
city run grocery stores should be expected to make groceries more expensive, not less expensive, because you're increasing labour costs by taking on government employees and because you're no longer operating at economies of scale. the premise that the idea is based on, which is that grocery stores are running a business model based on price gouging, is demonstrably false, or at least it is when it comes to actual groceries. regardless, the cost inputs to get a city to do this increase over a grocery store, they don't decrease.
it follows that the store is either going to be unable to compete with the private sector because the prices are too high, or they will mark everything down, take a loss, and pay for it with tax money, rendering the whole thing as a stupid, expensive, performative waste of time.
the money would be better spent on government food bank donations. while i don't think government should run grocery stores, i do think that governments should be running food banks, and it bothers me that this is left up to charity when it's something the state should clearly be doing, and doing better.