What if Himmler had Heydrich assassinated before the coup attempt against Hess?
What if Himmler's coup had been successful?
Well, Himmler's coup was not exactly for Heinrich to become Führer, but for him to eventually become one by ridding Hess of his allies, Heydrich was able to achieve that halfway but his greatest mistake was forgetting Wegener and instead killing Klopfer in the second night of the long knives. If Himmler's coup succeeds, he can rid himself of Goebbels and the Control Faction, intimidate Speer into cooperation and get rid of the traitors in the Wehrmacht all at once in the best case scenario while all Hess will know is that reactionary officers in the military killed all those people and Himmler saved him.
Himmler will seek to fulfill his ambitions in expanding the SS to every aspect of German Society as an elite force to serve as the Vanguard to National Socialism. Through the "Circle of Friends of the Reichsführer-SS" and with Speer forced into "deepening" his SS partnership on Himmler's terms, the economy would be taken over by the SS with the leaders of some of the most powerful corporations on planet being members of the SS and with Himmler achieving his dream of creating the SSF by officially merging the Police and the Security Services. He had a proper vision for the SS in his mind that Heydrich mostly copied just for his own selfish goals to become leader one day. The Werhmacht would be slowly scaled down while the Waffen-SS would be built up as a replacement instead of being just a few divisions scattered around.
Eventually by the mid 50s I can see Himmler getting rid of Hess, a typical plane crash like the one that killed Todt, or Balbo, or Almirante...
When he becomes Führer, things will be harsher, Himmler will increase the pursuit of natality policies in the east which can lead to many relations of dubious consent at best with any Aryan-looking woman with SS men through programs such as the Lebensborn. I don't even need to say it but not only would Generalplan Ost not be stopped, but it would likely be intensified and centralized under Pohl's office of economic management in the SS as the offices of the SS become the de facto ministries of Germany. The Wehrmacht will end up fully replaced by the Waffen-SS over the course of the decade with nazified officers of the new Generation being put in charge of the new military force. There would be more incentive towards Pan-Europan ideals in the Pakt and Himmler would use Darnand's rule in France as an example, recruiting (by force if needed), millions of people from other states to serve a time in the Waffen-SS forces and eventually return home as ideal examples of the New Europe ideals that will be propagandized by the Pakt.
There is no question about it, Israel would be destroyed, maybe even during the 50s themselves shortly after the conquest of Iraq, a joint German-Italian-Syrian-Iranian-Arab force which would strike from all sides and eventually end up destroying the Jewish State and implement the Final Solution in there. I can also see the Ural War happening out of ideological goals, if Himmler will stand a better chance than Hess is... questionable, on one hand the armed forces will be unified and he will grant greater resources than Wegener could as the Reich is under his tight shadow grip, on the other, many competent Wehrmacht officers would have been gone. Similarly to Göring, I see the SS using the Black Market and controlling it rather than cracking down on it like Goebbels, Wegener and Speer would have wanted, there would not be an invasion of Portugal but the German influence over it would only grow through their connections in Lisbon.
About the Church, Himmler certainly was personally the most opposed to Christianity, but he was not as radical in how to fight it like the Control Faction and Goebbels would do, he probably would follow Hitler's instructions from the Table Talks and only keep a soft suppression for Christianity to "eventually fade". He would be fine with the Status Quo and the 1956 purges would likely be in a much smaller scale and less public, at most he would work it from a legalistic perspective and accuse the more outspoken priests of crimes such as sexual abuses and corruption. If Stephen X still comes up and starts to denounce Germania, he will work to undermine him and perhaps to assassinate him in a quiet way, sending a message to the Conclave to elect a more "reasonable" leader. Himmler would be overall much more insidious than Goebbels was, the way he approached the Holocaust compared to Goebbels shows that (Death Camps compared to the Kristallnacht, a more quiet, industrial and "impassionate" massacre compared to a non-stop pogrom).
Himmler would be a supporter of the Arabs and likely seize the chance to fight Britain, would he go ahead for a Third World War? It is very probable, but also he would prioritize his self-preservation and would keep postponing the war indefinitely due to the risks involved. People show their true character when backed into a corner and we do have an example in our world, when facing defeat and death, Himmler was willing to sellout Hitler and made secret plans for his own preservation instead of continuing a suicidal struggle in Berlin like Goebbels did. People like Goebbels are more dangerous than people like Himmler, because they are so fanatic that they have no sense of self-preservation, no way of talking them out of unleashing a nuclear war if that is what they believe is righteous.