Otto, you have one key misconception regarding the 737 systems. In any single channel approach a press of TOGA for any reason immediately disconnects the autopilot.
For a hard windshear warning (two tone and WINDSHEAR), the drill is to push TOGA then disconnect everything and apply maximum (full forward stop) thrust.
For an activation of the Predictive Windshear system on the radar a normal go around or the Windshear escape manoeuvre is at the captain's discretion.
We do not know what was attempted but in either cause, the autopilot would be disconnected the moment TOGA was pushed.
A single push of TOGA with the AT engaged annunciates GA in the FMA and the AT commands thrust to provide a rate of climb of 1-2000fpm (typically around 85-90% N1)
A second push of TOGA annunciates N1 in the FMA and you will get all 26k available at which point you will be climbing like a homesick angel at light weights.