Can be done fully manually or fully automatically.
In busy ATC environments where it becomes apparent that a G/A may be required, for workload management the A/P may be engaged (if not still engaged) in anticipation and the actions re-rehearsed together as a crew to avoid a c*ck-up. If in the late stages of the flare something happens requiring a go-around, unless auto landing, of course this will be flown manually.
However, regarding manual- or auto- thrust, on the A320, whether manual thrust at G/A initiation or not, once the thrust levers come back to the CLB gate after the G/A, the A/THR will automatically re-engage.