Except in the “New findings” part at the end, the BEA update report is sliced into paragraphs that start with a time stamp. Each paragraph contains details like general configuration of the flight (e.g. speeds, AoA), sidestick controller inputs, audio alarms, tidbits of dialogue between pilots where and when BEA thought the information significant. Clearly what is exhibited in each paragraph was observed between the initial time stamp and the time stamp of the next paragraph.
With this in mind and noting that between 2 h 10 min 16 and 2 h 10 min 50 (citing the report) “The PF made nose-down control inputs”, I venture to submit that it is quite unclear what exactly caused the zoom climb to 37500 ft and this is a hint that BEA intends to closely examine this point.
Whether it was pilot induced or something else, this phase of the accident played a major role in establishing the confusion that followed.