What is my training score the mean_train_score or mean_test_score?
The mean_test_score is actually the mean score of the validation step for each fold. The "test" word is probably not well chosen by sklearn in that case, if you want to make the distinction between validation and test.

However, I don't think you are totally finished here, and you should therefore not compare mean_train_score with the test core.

Indeed, the cross-validation phase gives you the best set of hyperparameters (case with maximal "test" score, which is actually a validation score), but you should not keep the corresponding model, especially (but not only) if the training set has few observations or there are few folds.
You should instead re-train your model a last time, with this set of hyperparameters, but over the entire train set (not only the $\frac{k-1}{k}$ cases used during cross-validation). This trained model will give you the training score (over the whole training set) and the test score (over the test set).