You are correct that Food Inflation is at the same level as the broad Inflation right now.
However last year when inflation peaked, Food inflation was 10.4% Y-on-Y (source, see 3rd chart) whilst broad inflation was 6.5% (source).
Meanwhile wage growth was at around the 6% mark (source) so below even broad inflation.
Looking at the graphs in all 3 sources, the higher than inflation average wage increase at the moment (even if it was evenly distributed across all income ranges, which in the present day US it is almost never the case) isn’t enough to compensate the already baked-in higher food prices due to the food inflation last year and the first quartile of this year.
Given that when people get overextended they will first draw down on any savings they have and cut down on non-essentials, and the problems that Target now pointed out didn’t just start today, it makes some sense that what they’re seeing is the reflection of an accumulation the effects from above wage growth inflation from April 2021 to early this year which was worse for Food during most of that period, significantly so at its peak.