Adam is considered the easiest optimizer to tune, though other optimizers can achieve higher performance with more hyperparameter tuning effort. It often works out of the box once you figure out the right learning rate. So it would be surprising if Adam would continue to flat-line after you tune the learning rate (assuming that there aren't bugs with your setup).
Looking at your plots, I think it's possible that your Adam-trained classifier is always predicting the same class (maybe class zero).
Evidence: Classifier converges very quickly to 25% training accuracy, which is unusual, and corresponds to the class balanced proportion of any one label. ~43% validation accuracy, corresponding approximately to the unbalanced proportion of class 0 or class 1.