Cereal we get the plainest muesli (no added sugar or salt, mostly flakes and grains with a lowish % of nuts and sultanas, I actually add a couple of handfuls of extra sultanas to the entire bag and mix it up), I soak it the night before just in a tub measure out how much muesli he will eat then pour on some milk until it barely covers the top, by morning everything is soft and mushy rather than hard and chewy. Some muesli is very high in sugar even those without added 'sugar' have high dried fruit content which means it is not fantastic for teeth although dried fruit has nutritional value that sugar doesn't so I personally prefer the dried fruit over pure sugary cereal iyswim. I actually bought a high fruit content for a few months for DS to get him onto the adult muesli (from a baby muesli which I think was quite sweet, it had dried fruit but was all kind of ground down) and then reduced the fruit content because we have dramatically reduced dried fruit intake for him.
omelet, French toast (eggy bread) or home made scotch pancakes or mini muffins made sugar free are good for breakfast. Again I don't know if you are looking to cut out dried fruit too...you can make pancakes with ripe fresh banana without dried fruit, same with muffins, or with grated fresh carrot, sweet potato or apple/pear to give sweetness. If your kids are used to very sweet things you could start with a batch that has a couple of prunes or handful of sultanas whizzed into the mix to make it sweeter but later on cut that down/out.
White bean cupcakes
choc kidney bean cup cakes
If you are happy to switch to dried fruit you can half dip dried apricots into chocolate, it's not something I'd do every day, about once a year perhaps but they do look very special and like a big treat.
I saw a thing on Jamie Oliver site which was a snickers bar made out of tahini, almond butter, I think it had date syrup (which is going to be really sweet) and nuts in, dipped in choc. There are all sorts of variations on-line for healthier versions of bars/sweets although I haven't tried any.
Pasta sauce we make our own either with a can of plum toms or chopped plum toms or a carton of passata (it is 100% toms and nothing else, the low price shop brand is only about 35p) and we just use chopped onions, garlic, herbs, the toms and then whatever veg we are using. It's really not hard to switch to passata from a branded jar of pasta sauce, well I don't think so, and then you know a ton of extra sugar hasn't been thrown in.
Red pesto is not too hard to home make. A jar of roasted red peppers whizzed with nuts (or ground nuts), garlic, some oil from the jar of peppers and stir in grated parmesan.
DS's snacks are usually fresh fruit or a carrot cut into batons (they given them whole carrots at school and don't peel or anything so that's super easy!). Sometimes he has a couple of crackers or a pack of mini cheddars or a piece of cheese or he might ask for cherry toms or cucumber instead of fruit.
Occasionally dried fruit or a biscuit for snack.
We use regular ketchup tbh, because our general diet is not high in sugar or processed foods I am not bothered if DS has a spoon of ketchup or bbq sauce sometimes, I don't encourage it but if he asks for it I don't glare at him either