I see that when the altitude returns to the same as it was at the beginning of the event (red arrows), the airspeed has also returned to the same or a very slightly lower value.
This means that
very little enery was gained/lost overall from the up/down draughts during this period of 32 seconds, although at the end of this time (at 12m 32s) the elevator was full down, the AoA was -11 degrees, the aircraft was pitched 90 degrees down, and the crew was experiencing a negative 2.5 g acceleration. All this with little or no change in total energy.
Isn't almost no change in total energy (potential + kenetic) during altitude excursions a characteristic of a phugoid?
Of course once the crew intervened it ceased to be a simple phugoid, but there was still negligible overall energy input from the up/down draughts.
Cheers,