Germany likely would have experienced serious economic problems if WW2 hadn't happened. Around '37 or so the government faced a choice between returning to foreign trade and pursuing informal economic domination of central and eastern Europe, or going all-in for rearmament and great power war. Hjalmar Schacht resigned as Economics Minister in '37 over this issue when he had basically been replaced by Goering, a Hitler sycophant with little economics background. Hitler also dismissed Schacht from the Presidency of the Reichsbank in 1939.
With Hitler gone, I'd predict massive inflation or a rise in black market activity that might be cracked down on by the Gestapo. Germany tried to avoid the demand-pull inflation that can come with massive government spending through wage and price controls, but those would only work for so long without a war economy to suppress consumer demand.
The Nazis might fall from power due to a combination of hyperinflation and a succession crisis after Hitler's death that fractures the NSDAP elite. Any militarists and non-Nazi nationalists left in positions of an influence might boot the Nazis out of power and create a military dictatorship. The closest OTL example to this is similar the Romanian establishments's attempts to co-opt the Iron Guard and use its popular support, followed by Antonescu's crackdown on them in after an attempted Guardist coup in early '41.
A less harsh authoritarian regime authoritarian government like the Sanacja government in Poland or the royal dictatorships in southeastern Europe was the common form of government at the time. It would be interesting to see Central and Eastern European politics without WW2 and communism, there could be a long period of stable authoritarianism like Franco or Salazar's governments, or a revolving door of military coups and elected leaders like in Thailand and parts of Latin America.
If Germany's really lucky, the right-wing authoritarians would fall from power and something resembling democracy could take its place. If the Reichstag Fire Decree and the Enabling Acts are repealed by whoever succeeds Hitler, there is a legal basis to return to the Weimar Constitution.