Your sauce will still have less sugar than others, but if I understand correctly, simmering for hours will break down the more complex sugars in tomatoes into simpler sugars resulting in a somewhat sweeter taste

I think cooking does also dull the percieved acidity of food though, hence lemon juice or other acids often being added at the end so as to keep the brightness. But I'm not actually sure if the pH changes or if it's just a change in the tartness we associate with acidity, maybe someone can chime in with more information :)

Not sure about the jar portion. But the caramelization process is a bit complicated. It uses free sugars and amino acid to make the brown, caramelized flavour.

Onions are ~9 % carbohydrates with 4 % of that being simple sugars capable of caramelizing. Apparently another 2 % is fibre, leaving ~3 % being more complex carbohydrates I guess? Like cellulose or starches maybe. Those can get broken down at some points, but as far I know, need enzymes to do so.

But back to your question, if the small glasses are showing "sugar" as in sucrose, the onions could have either sucrose maybe? Or individual sugars such as glucose and fructose (the 2 components of sucrose). There's a number of other single sugars that could make up that 4 % though.

My grandma's old recipe was just letting them soak in it all day and then taking them out rather than leaving them in. They're a very nice snack after soaking in there. Very interesting flavor.

I'm a fraud