https://books.google.de/books/about/Führerlos.html?id=LjMhAQAAIAAJ&redir_esc=y&hl=de
There is an excellent alt history book about it. Unfortunately it is in German only I think.
Hitler is killed in 1939 (Poland is already conquered) and Elser succeds.
Göring acts quickly and takes the power via the "Ministerrat für Reichsverteidigung" (Minister's council for national defense).
The SS is quickly neutralized by a decisive action of Luftwaffe ground troops. It is clearly laid out why the SS could never take power and why neither Himmler nor Heydrich were more than functionaries before the late war.
Göring achieves a peace deal with the west and secures power by bringing back the Kaiser and going through with the Volkswagen scheme. He goes "soft" and reigns the Gestapo in. The Kaiser tries to actually influence policies but Göring makes it clear with rather brutal methods that the state is National Socialist.
War with Russia still happens because the final solution is not possible in peace time while the world watches.
I am not a particular fan of the whole "the Kaiser comes back" subplot but here it makes sense because Goebbels tries to secure power with "Hitler's heir". Eva lied about being pregnant to stay relevant and when Goebbels realized it was lie it was already to late. Göring countered that by bringing back Wilhelm as an identification figure.
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Using this plausible scenario as a basis (minus the plott stuff like Eva's pretend pregnancy etc.):
Göring is even more likely to achieve peace in the West. He holds all the chips in 1940 and is willing to make substantial concessions.
The "Ministerrat für Reichsverteidigung" (council from here on out) probably becomes something similar to the post-Stalin Politbureau. There is a strongmen but several factions wield real influence on policy making. Everyone is trying to prevent the rise of another "absolute ruler".
The Council is where the decisions are made but just like in the Soviet Union there is a parliament as a smoke screen.
The new strongmen won't be called Führer. He will either be "Reichskanzler und Reichspräsident" or will have his own title. "Reichsmarschall" or "Reichsverweser" are good examples.
Persecution and genocide are complicated topics. Sinti and Roma, homosexuals, Jehovas witnesses, Socialists and Communists and other persecuted groups are still killed or "slowly killed" in concentration camps without a doubt.
There is a strong argument that Göring as one of the architects of the final solution would have done something similar to OTLs Holocaust.
I would argue though that in Görings case there is the possibility that he wasn't an ideologue but saw an opportunity to get more power by controlling the process of the Holocaust. So we might see a TL were jews are "merely" being treated as in OTLs 1939/1940 (see the quotation marks, they would be essentially forced into Ghettos in Poland to slowly die).
Interesting for a TL could be a scenario where Göring makes it one of the conditions of a peace treaty to get rid of the jews. Essentially "we pull out of France and Benelux but we get repearations and you have to take all the jews from lands controlled by Germany".
It is anybodys guess what Göring would have done as the man in charge. I would just say that we can't forget the massive pressures in the NSDAP to "solve the jewish question".