Is using the left hand to count tasbihs and adhkar, while seeking forgiveness and glorifying Allah with the right hand, considered an innovation, especially if the purpose of counting is to know the daily amount of dhikr in order to increase it when it is little, and to maintain the continuity of dhikr?

As for the adhkar (remembrances) for which a specific number has been prescribed in the Sharia, it is permissible to count them with the right or left hand. It has been reported from the Permanent Committee that counting with the right fingers is better, and counting with both hands is permissible. As for the absolute adhkar, the principle is to recite them frequently without a specific number. However, there is no harm in counting them, especially for a valid purpose. It has been reported that the Companions and the Tabi'un counted their adhkar. Ibn Mas'ud's disapproval of a group engaged in tasbeeh was due to his disapproval of their manner of gathering, not merely the act of counting.