More to the point here - if people are eating out more and shopping for groceries less, that would result in grocery prices *dropping*, not rising. While food is nominally fungible, if people eat out more, then restaurants can raise prices (increased demand for their product) and grocery prices will drop (reduced demand for their product). Grocery prices were not dropping - because the issue was production and supply chains.
The food services that supply restaurants either are—or compete directly—against the distributors that supply grocery stores. Those services buy from a handful of middlemen that buy the actual food from the actual producers.
If one segment is taking more of the product, they shuffle it between the two. The price goes up because of overall demand on the suppliers, not just one mode to market or the other.
Restaurants and all the other things I listed consume more food than people buying groceries and cooking them at home. So more of that activity means more food demand than people only buying groceries and eating at home.