Things that can happen when you lose the tail
It is fairly clear that the tail came off/ apart while inflight.
One of the major functions of the tail is to supply down force to balance the wing's pitching moment. If the tail is suddenly removed, the aircraft will pitch down abruptly and its pitch rate momentum may be sufficient to carry into another cycle if the initial pitchover does not destroy the wing integrity/symmetry completely.
Another function of the tail is to minimize yaw. With sufficient yaw, the static system may become pressurized by dynamic airflow causing altimetry measuring systems to indicate too low and rate of climb indications to go strongly negative. Likewise, if the aircraft then momentarily points back into the airflow, altitude will appear to increase and rate of climb will go strongly positive.
Once the aircraft pitches strongly nose down, deceleration will be extreme, and the inertial system will respond assuming it is still powered. The only source of electrical power is the engines, and the loss of data at ~FL280 is probably indicative that the engines were shed at that point. The RAT system probably would not function in such a chaotic environment.
One characteristic of Airbus C* aircraft control systems is that they attempt to maintain their velocity vector direction until disturbed by an outside force. The slight decrease in climb rate at 04:12:34 might result from air venting through a fuselage rupture causing a net nose down force.
Structural failures can be instantaneous, but frequently there is a cascading breakup sequence. I suspect that there was such a cascade of failures in this case leading to the obvious departure from controlled flight.
The FR24 data should be looked at in this context.