Generally they look at both and publish both

Food and Energy are generally impacted by different factors than consumer goods, but a spike in one of those two could mask the behavior in consumer goods so most inflation charts actually look at 4 things

All items

Food

Energy

All items not including food and energy

If food costs start to climb 9.5% due to a specific set of circumstances but the rest of things are only growing at 5.5% then how much is inflation impacting people? It depends what percentage of their budget is food. The standard weighting for "All items" has inflation at 6% but that really masks the impact that high food costs have on lower incomes and the less significant impact they have on higher incomes.

Its also important to track energy separate because energy costs feed into other goods. If electricity costs increase 10% then that cost gets passed forward in the cost of other products since they now cost more to make so its important to be able to see it as both an input cost and as an end impact on the prices