Compared with those in the lowest quintile of UPF consumption, those in the highest quintile had an increased risk of depression, noted for both strict definition (HR, 1.49; 95% CI, 1.26-1.76; P < .001) and broad definition (HR, 1.34; 95% CI, 1.20-1.50; P < .001) (Table). Models were not materially altered after inclusion of potential confounders. We did not observe differential associations in subgroups defined by age, BMI, physical activity, or smoking. In a 4-year lag analysis, associations were not materially altered (strict definition: HR, 1.32; 95% CI, 1.13-1.54; P < .001), arguing against reverse causation.

"Found a link between" typically is pop science speak for small p value. Not that I would take it for granted that it does, so you should just read the paper if you have a question about the details: https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10512104/