Does adding new features that contain information derivable from current features help performance? So say you have some data that consists of some values:

1.3, 0.9, 1.1

You introduce a new feature which is the average of these values: 3.3

In this example lets say that you know the average of these features is a good indicator to classify data with. My question is that, you're not actually adding anything to the model by creating this 4th feature, all the data is already in the features so does having this average help the model training identify the relationship more easily?
It depends what model will you train and depend on the new feature. However, your answer is that yes. it is possible to help the performance of that model. For example, suppose the new feature is a non-linear combination of other features (multiple of the other feature) and your model is a linear classifier. When you add the new feature might help to classify better the data depends on the context.