when dealing with optimal monetary policy, central banker does not consider IS equation both under discretion and commitment? In most cases I see the following form,

I am referring to Gali’s textbook (2nd edition) example of 5.2.1 and 5.2.2. The optimal conditions are derived without IS equations as one of the constraints.

As documented in the book further down below, the DIS equation is an implementability constraint. It describes how agents react to interest rates with their consumption. In the basic planner’s problem, the planner simply chooses consumption. Hence, the DIS equation is not needed.