but “ultra processed” not defined by any metric

This is the shit that grinds me. You have the world's information at your finger tips and you're making a wild claim that there isn't a definition for something and basing your argument around that. You have gone this far in your life with the belief that there is no definition "but any metric" for Ultra Process foods?

Don't you think that's a little absurd to think this? I mean, it's literally in the word. Not processed – ultra processed; meaning, roughly, that the food or ingredients in that food are processed again after initial processing.

What I will grant you is that this word is sometimes thrown around inappropriately. You (and us all) have every right to be upset by this confusion and misrepresentation.

https://www.universityofcalifornia.edu/news/what-know-about-processed-and-ultra-processed-food

Category 4: Ultra-processed foods are industrial formulations made from food components. They include additives that are rare or nonexistent in culinary use, like emulsifiers, hydrogenated oils, synthetic colors, texture improvers or flavor enhancers. Think chips, soda, instant soup, pastries and mass-produced breads.

https://www.cambridge.org/core/journals/public-health-nutrition/article/un-decade-of-nutrition-the-nova-food-classification-and-the-trouble-with-ultraprocessing/2A9776922A28F8F757BDA32C3266AC2A

Ultra-processed foods, such as soft drinks, sweet or savoury packaged snacks, reconstituted meat products and pre-prepared frozen dishes, are not modified foods but formulations made mostly or entirely from substances derived from foods and additives, with little if any intact Group 1 food.

Ingredients of these formulations usually include those also used in processed foods, such as sugars, oils, fats or salt. But ultra-processed products also include other sources of energy and nutrients not normally used in culinary preparations. Some of these are directly extracted from foods, such as casein, lactose, whey and gluten. Many are derived from further processing of food constituents, such as hydrogenated or interesterified oils, hydrolysed proteins, soya protein isolate, maltodextrin, invert sugar and high-fructose corn syrup.

Additives in ultra-processed foods include some also used in processed foods, such as preservatives, antioxidants and stabilizers. Classes of additives found only in ultra-processed products include those used to imitate or enhance the sensory qualities of foods or to disguise unpalatable aspects of the final product. These additives include dyes and other colours, colour stabilizers; flavours, flavour enhancers, non-sugar sweeteners; and processing aids such as carbonating, firming, bulking and anti-bulking, de-foaming, anti-caking and glazing agents, emulsifiers, sequestrants and humectants.

A multitude of sequences of processes is used to combine the usually many ingredients and to create the final product (hence ‘ultra-processed’). The processes include several with no domestic equivalents, such as hydrogenation and hydrolysation, extrusion and moulding, and pre-processing for frying.

The overall purpose of ultra-processing is to create branded, convenient (durable, ready to consume), attractive (hyper-palatable) and highly profitable (low-cost ingredients) food products designed to displace all other food groups. Ultra-processed food products are usually packaged attractively and marketed intensively.