Great question. I can see how the use of words like “food” and “nutrition” can be confusing because they have different meanings to different people.

Here’s my joke answer: “If you want to make dinner, don’t you need ingredients?” Even if you are a very hard worker, you can’t make something from nothing.

Here’s a longer answer:
Everything is made of MATTER. When biologists talk about nutrients, we mean the matter that makes up building blocks of life. For example, atoms like carbon, hydrogen, oxygen, phosphorus, and nitrogen form the most important biological molecules (proteins, carbohydrates, fats, DNA, etc.). There are many other nutrients that living things (including plants) need in smaller amounts, like iron, calcium, and zinc. Plants take in their carbon through their leaves as CO₂ (carbon dioxide). All the rest, they bring up through their roots.

All life requires ENERGY. Autotrophs get their energy from light. The energy allows them to do work, like put the building blocks together into the molecules and larger structures (cells, for example) that living things need. Plants can’t transform energy into matter. Here’s an example. Plants make “food” like sugars and starches. The nutrients are the ingredients they need. The energy to take apart water and carbon dioxide, then put the atoms together into sugar and starch molecules comes from the sun.

So I have a question for you that will require you to do some research. If Venus fly traps do photosynthesis, why do they need to eat bugs?

You may be interested in studying plant ecology.

Autotrophs can make their own energy (or rather they get it from inorganic sources). They still need matter from elsewhere. Nutrients are matter.