the only data I have seen that is very compelling is from Israel where, you are correct, breakthrough infections are also making people seriously ill and they are dying. It seems to me, and others may refute this with good data, that illness burden increases at a certain rate but only mild illness initially. Over time, serious illness rates increase as well - it just lags as immunity is strongest the first few months.

First, there is primarily mild breakthrough infection and then, as the veil of protection diminishes further, severe breatkthrough increases. That is my take.