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The bags of flour I find usually list more, typically something like
After the common milling process tempers the grain, separates constituents through rollers & sieves to extract flour from endosperm, with coarser constituents (bran & germ) optionally ground up & reintroduced, it’s usually far removed from its natural state. Mills have existed for millennia.
Salt may often include an “anti-caking agent”. Ingredients for baker’s yeast may include some unfamiliar chemical compounds. Baking soda & sugar aren’t naturally found in the states they’re used for baking. Oil is often pressed from some seed & filtered. They’ve all been prepared in controlled conditions that yield an unnaturally pure state.
Unless the bakers are sourcing unbroken wheat & raw ingredients, then mashing it themselves into something ancient Mesopotamians might have made, they’re probably starting from some highly processed ingredients.
Nutrition resources linked in other comments typically identify bread as highly processed.
Processed ingredients can be okay with all these things, too.
While the bakery bread could be better in some way (we could be wrong), a word like “processed” explains it poorly.
I get your point that the word means something. I took claims regarding processed food seriously, then found the idea unsustainable when close examination indicates nearly any prepared food we’d consider healthy also classifies as processed, sometimes highly. While some types of processing are unhealthy, there ought to be better ways to identify them.
As you said bleached white flour has been a thing for a very long time, it is considered traditional, people generally don’t include things that have been common for millennia when they think of “ultra-processed”, I actually mentioned this in previous comments. The only other ingredients are vitamins/minerals, you definitely can get bread that isn’t enriched, but again, very few people believe adding a couple common vitamins to basic food is “ultra-processing”.
Also, depending on how into bread your bakery is, some do get unprocessed wheat corn and work it to the product they want, though I have only seen these in major cities, that can support boutique bakeries, that have Michelin stars . Most will offer non-white flour options that are significantly less processed, and multiple different levels of processing, for the various specific type of bread they are making.