"Very little fiber", "Frequently have a lot of oil", and "Relatively high in salt and sugar" aren't a classification, they're vibes.
What you've listed aren't classification criteria. These are generally common characteristics within the category, and a basis for investigating what causes ultra processed foods to generally be bad.
I'm in this thread arguing that the scientists have the data to be able to just analyze correlations and trends of those characteristics directly, rather than taking the dubious step of classifying them into the NOVA category to begin with.
It's not pseudoscience or not science though. The models are the models, and I think they're bad models, but I don't think they're outright unscientific.
But what confounding variables have also increased during this time? Do we have endocrine disruptors in our drinking water or food packaging or in the foods themselves, from microplastics or whatever? Have we been fertilizing our fields with industrial waste containing toxic "forever chemicals"? Have we become more sedentary at home and at work? I mean, probably yes to all of these.
I do believe that nutrition is more than simple linear addition of the components in a food. But insights can still be derived from analyzing non-linear combinations (like studying the role of fiber or water or even air in foods for the perception of satiety or the speed that subject ingest food), or looking towards specific interactions between certain subsets of the population with specific nutrients. We can still derive information from the ingredients, even if we move past the idea that each ingredient acts on the body completely independently from the other ingredients in that food.
And look, I'm a skeptic of the NOVA system, but actually do appreciate its contribution in increasing awareness of those non-linear combinations. But I see it as, at most, a bridge to better science, not good science in itself.