Recently infected people haven't had as much chance to succumb. There are also delays in reporting I believe. I also think your explanation carries much of the effect size, but the timing also matters.
It’s not about recently infected. It’s about deaths per day of unvaccinated. If the amount of death among the unvaccinated is going down daily then it is. It has nothing to do with recently infected because at some point some of those people may die next week or the week after and it will be reported then.