I agree reporting bias could be a thing, but there are statistics like completed suicide which are less susceptible to it (though still present; you can imagine a suicide being declared an accidental death to help a family "avoid embarrassment"). And those statistics have also been steadily creeping up for decades.
I think reporting bias should be the starting point and the primary area of inquiry when looking at this topic. Unless I'm imagining the recent past where mental illness was literally verboten to speak about and mental health services were widely derided as scams. The change in discourse has been as rapid and dramatic as any social change I can think of, yet the authors seem to think it's enough to simply acknowledge that and focus instead on their many charts, most of which are about self-reporting or diagnoses.
I don't think many people are still calling therapists "quacks" and extreme things like that. Though I'm sure there's some Boomer men keeping that tradition alive.
Some of these issues are solved! People seek help, or are referred to help, and they get help. The article is showing in part that more people are seeking help, not that they're not getting help.
Though with minimal mental health funding, any kind of sustained help is out of reach for most people.
And speaking of men, it doesn't surprise me that the data is showing a larger increase among women. Men really seem to fetishize "handling things themself" and that kind of nonsense.