What is the ruling on someone who prays Dhuhr, then sits for a gathering of remembrance (dhikr), then returns home to pray the Sunnah prayers before and after Dhuhr (Qabliyyah and Ba'diyyah), and does this once a week?

Performing supererogatory prayers at home is better than performing them in the mosque, provided that the time for the obligatory prayer does not elapse. A gathering for dhikr, if it is a gathering for learning or for admonition and guidance, then it is good. However, performing adhkar in a collective manner is an innovation (bid‘ah).