Hitler's prestige within Germany was strongly bolstered by his ability to unwind provisions of the Versailles treaty. For example, the remilitarization of the Rhine valley (demilitarized by Versailles), the annexation of Austria (forbidden by Versailles), or the reestablishment of military conscription.
So yes, it is true that it gave Hitler prestige put Hitler had already a lot of control of the state and was already preparing for war at that time.
The war happened because Hilter and co wanted war. Hilter came to power because of a economic crisis. The rest is just Hitler gambling again and again, not the root cause.
The treaty directly led to the economic crisis which led to Hitler coming to power; even if the treaty was dead by then, it's work in setting the stage for WWII was done.
Both the hyperinflation and the great depression did not happen because of war payments, maybe one could argue the german political class did stupid things because of the treaty.
WW2 happend because a fascist party managed to gain power after the greatest economic crisis in german history. This is somewhat related to WW1 and the Peace Treaty but saying the Peace Treaty is the reason is not substainable.