Feature extraction helps the model learn useful information from raw data. The key metrics to check are accuracy or loss on validation data. These show if the extracted features help the model make better predictions.
For classification tasks, accuracy, precision, and recall matter because they tell us how well the features separate classes.
For regression, mean squared error (MSE) or mean absolute error (MAE) show how well features predict continuous values.
In short, metrics that measure prediction quality after feature extraction are most important. They tell if the features are meaningful.