The depression ended a couple of years after the war
The common view among economic historians is that the Great Depression ended with the advent of World War II. Many economists believe that government spending on the war caused or at least accelerated recovery from the Great Depression, though some consider that it did not play a very large role in the recovery. It did help in reducing unemployment.[11][101][102][103]
When the United States entered into the war in 1941, it finally eliminated the last effects from the Great Depression and brought the U.S. unemployment rate down below 10%.[105] In the U.S., massive war spending doubled economic growth rates, either masking the effects of the Depression or essentially ending the Depression.
https://en.wikipedia.org/wiki/Great_Depression#World_War_II_and_recovery
If you define depression by unemployment rates, yes, WWII ended it.
But living standards DECLINED during the war. What good is lower unemployment if you can’t buy things, travel, etc.? That’s Soviet economics. The USSR & Cuba bragged about their full employment.