mjhjmtu

I'm not sure if this belongs here or in the English language stack exchange but here goes:

We have broad classifications like "Fruit" and "Vegetable" and "Meat"/"Protein". What do you collectively call bread, rice, pasta, cereal etc. My first guess was "Grains" but that feels like referring to the unprocessed thing rather than the food.

There are several terms which you can use, depending on the context of writing (or speaking).

A very simple one is "the starch". It is mostly used in the context of meal planning, such as "What starch are we going to serve tonight" or "When planning a vegetarian meal, it is best to first decide on the starch and then select sides that complement it".

"Grains" or, mostly interchangeably, "cereals" is what academic specialists for nutrition and diets use in their jargon. If you read a textbook on nutrition, that's where you will find breads, etc. There, the context makes it clear that the word doesn't mean simply uncooked kernels. The nonacademic literature on dieting is more likely to use "carbs" - see Chris H's answer for more detail on that usage.

In legal language, for example rules and regulations about food product labelling, or import and export regulations, you will frequently find phrases like "grain products".

Since none of these terms is unambiguous, outside of these genres of writing you will probably have to go for something more descriptive, for example "foods made from grains" in a colloquial conversation.

A broader category, including things like potatoes, would be carbs (carbohydrates). This is a common category when considering feeding for exercise, and tends to mean starchy foods. It's not a perfect term as "carbs" strictly includes sugars, but the carb component of a meal is the (usually fairly plain) bulk accompaniment to the tasty bits.

Since all of those, specifically (even the bread) are derived from cereal grains, they are generally referred to as "grains."

Any food made from wheat, rice, oats, cornmeal, barley or another cereal grain is a grain product. Bread, pasta, oatmeal, breakfast cereals, tortillas, and grits are examples of grain products.

Grains are divided into 2 subgroups, Whole Grains and Refined Grains. Whole grains contain the entire grain kernel ― the bran, germ, and endosperm. Examples of whole grains include whole-wheat flour, bulgur (cracked wheat), oatmeal, whole cornmeal, and brown rice. Refined grains have been milled, a process that removes the bran and germ. This is done to give grains a finer texture and improve their shelf life, but it also removes dietary fiber, iron, and many B vitamins. Some examples of refined grain products are white flour, de-germed cornmeal, white bread, and white rice.

US Department of Agriculture: What Foods Are In the Grains Group?

Starch

I've heard it called the Rule of Three - protein, starch, vegetable.

The first thing that came to my mind is that these are "staple foods." In other words, and especially for what you specifically mention, these foods constitute the basis of diet for a group of people.

Of course, they're also starches, carbs, sugars, etc.