Is there a reward for my sitting in the mosque—after the prayer and finishing the adhkar and sunan—or is it like my sitting in any public place?

The angels seek forgiveness for the worshipper as long as he remains in his prayer place where he prayed, as long as he does not invalidate his ablution or cause harm. They supplicate for his forgiveness and mercy. This includes anyone who sits without engaging in anything, but being occupied with remembrance (dhikr) and reciting the Qur'an is more complete.