I think the Nazis are going to stick to the script so to speak. Goering is the designated next Fuhrer according to Hitler so Goering gets the job. Bormann will probably kiss up to Goering and talk about carrying out Hitler's wishes. he probably gets banished from the new Fuhrer's court as soon as the smoke clears and eventually end up dead in some prison. Goebbels will be another one who sucks up to Goering so he can keep his position of power.
As for Goering himself I think he becomes more of a figurehead rather than a micromanager like Hitler. He will let the Army do what it wants in exchange for it's loyalty.
No one has mentioned the Kriegsmarine. I guess they will carry on with fighting a losing battle in the Atlantic. They will side with the Army in supporting Goering.
Himmler and the SS will concentrate on killing traitors real or imagined as OTL. I don't think Himmler will make a grab for power. What I think will happen is that the SS will start trying to cover itself up for all the wartime atrocities committed. Himmler might order the dismantling of Auschwitz and other camps. At the same time the SS start liquidating prisoners still living. You might also see people who literally know where the bodies are buried start disappearing or sent to the front.