You are indeed overthinking this. It flys like a normal aircraft, and the trim effectively works the same.
The auto throttle has nothing to do with this function.
If you are flying level, the flight control system is maintaining an attitude to maintain a speed, the trim ref. speed.
If you trim nose down, the trim ref sped is increased, the attitude is adjusted to maintain the new ref. speed and the aircraft will descend, maintaining an attitude to maintain the new trim ref speed.
If you change the attitude but do not trim, the ref speed is unchanged, so eventually, the flight control system will find and maintain an attitude to maintain the trim speed. In this case it will be the same attitude and speed as before the disturbance.
All this assumes constant pwr/ config.
If you just increase the pwr. The ref speed is unchanged and the aircraft will fly an attitude to maintain it, ie climb.