In the long run, it might prove a mixed blessing. A retired Pope could be either irrelevant or influential, and there could be trouble if the incumbent and the retired are in strong disagreement.
Think of how many Japanese rulers exerted most of their de facto power as retired emperors or retired shoguns.
It would likely, however, improve the overall governance of the Church somehow, avoiding senile Popes who let curial conflict and corruption go unchecked.
It really go either way, or both.
A retired Pope could probably focus on intellectual work if he doesn't choose to just stay away in some monastery and pray unnoticed. That could shape theology in interesting ways, though probably in general encouraging conservative views (a book by a retired Pope would probably get wide audience and high regard).
But I am not sure.
As for the Holocaust thing, a retired Pope would probably share the same concerns Pius XII had IOTL that induced him to prefer discretion; otherwise, things could get very, very messy. A vague possibility is that the incumbent Pope deems safe enough to let his retired predecessor to speak out loud, a sort-of "plausible deniability" since the retired Pope is no longer speaking as the leader of the church, so removing in part the fear of outright persecution by the Nazis that operated in IOTL.