what exactly the restaurant is objecting to if I am not buying a separate meal for my child. They're still "freeloading", using chair, table space, cutlery, etc
Surely the point is that if they allow a toddler to bring in their own food, at what point do the draw the line? A 3 year old? A 10 year old? A particularly fussy adult? It's simpler for a restaurant to just have a blanket rule on no food to be brought in, even if no extra food is ordered as a result. And it's probably much easier for the restaurant to turn a blind eye to a nibble on a breadstick or rice cake than it is for a toddler to be eating a home cooked pasta meal as in this case.
yes, I think it's fine to feed my baby (not myself as you switched it it) my own formula, purées, breastmilk, water, drinks, snacks, breadsticks, crackers, teeny tiny pots of three course meals, what the fuck ever, if (a) there is no sign to the contrary, and (b) I am buying meals for everyone else.
Why should there have to be a sign to the contrary? Surely it's just common courtesy to check before you crack on with feeding your child? If the OP had checked, then she could have chosen to stay or leave before she ordered anything, and the whole problem could have been avoided.