As the parent of two mid-20's adults (one thriving, the other not so much) I actually downloaded the paper and read it out of curiosity (shocking, I know.)

They asked people how many days last month they had "bad mental health days" ("Q1".) The measure of Despair in the graphs is constructed as: "by setting the Q1 variable to one when an individual gave the answer 30 and zero otherwise." So if you had a continuous month of "bad mental health days" you are in despair. The fraction of those months is y-axis in the graphs (typically around 0-10%)

This is all US data BTW.

Anyway, the abstract and title oversimplify the data in my opinion. Across the board (even up to 60+ years of age) the surveyed report overall 2x more "despair" than in the 1990's. Yes, it is worse amongst under 40 workers, as shown in Figure 4. Despair used to be pretty flat by age for workers, now it it highest for young workers, with linear-ish decrease until about 60 where the value hasn't really changed over time.

But the graph in Figure 8 shows that "despair" hasn't really moved much for any age group of college educated workers since the 1990's. And their mention of the change in the "hump" shaped in the abstract doesn't account for the fact that in absolute terms, unsurprisingly, the unemployed have a lot more despair overall than workers.

So the "young workers" in the title are those without a college education in the US - that's probably a very different demographic than the average HN participant...