It is even worst. Your calculation is quasi-static.
And unnecessary complex. If external pressure at 4000m depth is 400 bars, the internal volume will become 1/400 of the original volume.
But the event was highly dynamic...
The shell parts were accelerated towards the center, were air and corpses were compressed. Due to inertia, the compression reaches a peak pressure several times larger than the external pressure, so in the maximum compression instant the inner pressure has peaked somewhere around 1000 bars (2.5 times the external pressure of 400 bars).
Perhaps even more.
So the inner volume of the shell was instantaneusly reduced to 1/1000 of the original value.
But as the compressed material is elastic, after reaching that very high pressure peak, the compressed material did expand back, projecting small chunks of the shell and its contents all around.
Only very hard parts, such as the titanium domes, could have survived the secondary explosion.