Which scoring for GridSearchCV is best, when imbalanced multiclass dataset?
There is lots of metrics to measure performance of classifiers. The fundamental ones are based on the idea of:


true positive (TP) — sample’s label is positive and it is classified as one
true negative (TN) — sample’s label is negative and it is classified as one
false positive (FP) — sample’s label is neg., but it is classified as positive
false negative (FN) — sample’s label is pos., but it classified as negative


From what I have seen in white papers, F1-score is the most used metric that consider in imbalanced classification scenarios. But I also see ROC-AUC as a frequent used metric. As I mentioned, there is lots of metrics, but I strongly recommend you to keep these most used to provide to the others some standard sense of performance.