The values under the column F1 don't agree with the formula. Any answers
It is not a bug just weighted averaging is used in computing F1, precision or recall. That means that score is computed per each label/class and then averaged. See the documention by sklearn.
In case of the classifier with 3 classes, the F1 score is computed for class 1 as a target class using the rule you wrote, class 2 as a target class and class 3 as a target class. Those scores are then averaged to retrieve the final score. Recall and precision are computed the same way, all of them are averaging over class scores. The rule you wrote is used in per class calculation but it does not hold for averages.