Is canned “tomato sauce” already cooked?
Yes, in some sense, the contents of a can of tomato sauce are already cooked. But "cooked" is a pretty vague term, and we know that there are different degrees of it. Did you cook your onion on a low heat until it was soft, or until golden, or until caramelised? Did you cook your steak until it was rare, or medium, or well done?

Likewise with tomatoes, if you blend them up and then cook them for ten minutes they're not going to taste the same as when you've cooked them for three hours in a low oven with the lid off. Lots of chemical reactions are going on inside the food as it's cooking, and some of them only happen over rather long time periods.

So what you're doing when you're putting the "cooked" canned tomato sauce in with your "cooked" meat and leaving it for a while is... cooking. The combination of ingredients plus more heat and more time will cause further changes and different flavours to emerge.

Also, canned tomato sauce will only be cooked enough to preserve it in the can - it's not been cooked to the point where it's going to be at its best for eating. That part's up to you.