Just been looking and manual reading. It appears to me like this. (Don’t mean it’s right would need somebody in long trousers to confirm

)
Your 2006 was basically the same as the L322 underneath. They seem to be a limited slip diff which can be fully locked or variable lock through electronic control. This all reacts differently in diff modes.
So I guess this is where we get to why you had no drive, I guessing for this all to lock up the car needs to see, 1 spinning wheel or mismatch wheels speeds between axles.
If you have a broken shaft you get no drive, no wheel speeds, so the brain does nothing.
Earlier models were fitted with a torsion type ATB which as above would give same results, in this situation too.
That’s my take anyway,
Sure somebody will put my thinking’s right if they aren’t
Don’t actually help fix your problem right now though
J