Is designating Saturday for group recitation of the Quran and completing a part of it weekly considered a Bid'ah (innovation), because it is specified, despite it being the most suitable day for the participants?

The method of reciting the Quran that you follow—where each person recites a section, and then the next person continues from where the previous one stopped until the designated portion is completed—is "management by the Quran," and it is a legitimate and commendable method. Imam Al-Nawawi mentioned that this is permissible and good, and Imam Malik was asked about it and said: There is no harm in it. Designating Saturday for this recitation circle is not an innovation (bid'ah), because your choice of it is based on its suitability for you as a day off and leisure, and not because you believe there is a special virtue in reciting on this day.