Worse AUC but better metrics (Recall, Precision) on a classification problem - How can this happen? I have two models on which I calculate train and test performances. They both are the same algorithm (lightgbm), same hyper-params, only the data differ (the second one has the data from the first one plus some more).
The first model returns 0.73 AUC with 0.32 Precision and 0.44 Recall (all these on the test set). The second model returns a considerably lower AUC (0.65) but with higher Precision (0.35) and Recall (0.66). Isn't that a paradox? Oh and if that matters, I should mention that the problem is imbalanced (10% class 1).

Remember that ROC curves are constructed by considering all thresholds, while metrics like accuracy, sensitivity, specificity, precision, and recall only use one threshold. When you configure your software to calculate the precision and recall of the models when the threshold is changed, I would expect you to find that the high-AUC model tends to outperform the low-AUC model.
However, it usually is preferable to evaluate the probability predictions, rather than applying thresholding. Two common ways of doing this are called log loss ("cross-entropy loss" in a lot of neural network circles) and Brier score. Frank Harrell has two good blog posts about this topic.
Damage Caused by Classification Accuracy and Other Discontinuous Improper Accuracy Scoring Rules
Classification vs. Prediction
Stephan Kolassa wrote a nice answer to a question of mine that gets at this topic, too.
Note that strictly proper scoring rules like log loss and Brier score need not agree about which model performs better (fairly easy to simulate), so it should not be expected that AUC and precision or AUC and recall agree on the better model, either.
