Hello.
The Airbus is normally flown the way you understand. On final approach following the GS, the sidestick is used to command changes in pitch and the resulting change of vertical trajectory. FBW system will trim the horizontal stabilizer automatically, and A/THR will adjust the engine thrust setting to match the target speed.
Thank you for the introduction. Knowing a bit about your situation makes answering easy and enjoyable at the same time. My generation and younger, almost all flew computer simulations before anything else.
Welcome to PPRuNe.