Observational studies, aka “epidemiological studies”, are studies that do not involve experiments. The independent variable is not controlled in advance, instead the samples are pulled from some population. Then you look for individuals within the population who exhibit whatever traits it is you’re studying. These types of studies are cheaper than controlled experiments, and often times the only type of study that can be ethically done.
These studies are good at finding correlations, but bad at determining causation. In the case of food-based studies, the population at large will typically have way too many confounding factors - you’re going to be introducing a ton of room for Bias as well.
Example
Observation: Population studies show that people who drink diet sodas are more likely to die of metabolic dysfunction.
Conclusion: Diet sodas cause metabolic dysfunction.
Reality: Perhaps people who like diet sodas are also the kinds of people who tend to eat other things that are worse for their health. You can’t really separate the independent variable from its gigantic litany of possible confounding factors.