What you provided is the steady state of the private sector equilibrium conditions, conditional on the value of the instrument. But that is not yet the steady state of the Ramsey problem. Typically, a steady state of that problem requires finding a value of the instrument that induces a steady state of both the private sector FOCs and the equilibrium conditions of the Ramsey planner. Take the labor subsidy in the New Keynesian model with monopolistic competition. Any value of the subsidy is consistent with the private sector equilibrium. But we know that the optimal choice of the subsidy is to exactly counteract the monopolistic distortion to have an effective markup of 0. If you start with a an initval of 0, you will end up with a different value that is compatible with a steady state.