What are things like Bread, Rice and Cereal collectively known as?

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.

The term "grains" is commonly used to referred to the 'processed' food as well as the 'unprocessed thing'. People often refer to 'eating grains', and they very rarely mean the unprocessed seeds.

I've also seen 'grain foods' used where there might be confusion.

The term "farinaceous" might be appropriate, especially when used as "farinaceous dishes" that include other ingredients. The corresponding noun "farina" isn't quite equivalent.

"Farinaceous" seems to be rare now but was more common in the 1800s.

The examples you've given are all from the grass family and they're examples of cereals. But if you included peas and beans, those are legumes or pulses.

But if you also included say potatoes then these are often called carbs.

It's unclear which way you want to categorise. If you want to reference the main bulk of some meal which a previous answer has called the carbs, I often call this the filler of a meal.

The term carbs can't really legitimately be used e.g. if your filler is a pulse such as kidney beans which has a high protein content so isn't just carbs. Again, bread is a filler but contains protein, carbs and a bit of fat. Or you have say dumplings which are another filler, this time often with a relatively high fat content.