Looks to me that the initial climb may have been due to a combo of flight through uplifting air, pilot induced pullup to avoid wx or possible a/c induced pullup due high speed, perhaps only flight director commanded if AP already OFF.
It's hard to see why else they would do that initial pullup and there seems to be a precedent in that other 'airprox' uncommanded pullup.
After that, when they ran out of energy, it seems clear that no-one on the FD realised that 'nose down' on the sidestick wouldnot be enough. They needed to trim.
Ah.....'trim' the basis of good piloting! Completely ABSENT in Airbus normal ops.
I mean, if you NEVER trim, how are you expected to realise that you are badly out of trim?