The federal reserve is acting just as terrible, mirroring their mistakes as well. Unfortunately just read they are pumping ANOTHER 1.5 trillion into the economy at the end of the week.
If I understand correctly, they did not actually inject any money into the market, they just released the Bonds that they hold over the banks.
Basically the government has tells the banks that they have to have x amount of security to before they can issue loans, the same way a bank holds security over you when you take a loan. They just loosened some of it, and will probably recall it later. No one actually got any money.
The Great Depression wasn't the fault of the government or the fed, it was mostly a natural occurrence, these things go in cycles. This one isn't really the fault of the fed either, it's mostly the fault of the pandemic, but also it triggered the burst of the bubble that had formed. The fed can make things worse but it's not the main cause and no matter what they did they couldn't stop it, they're in panic mode now. So it's much different from the Great Depression because this one had a specific "external" cause. It's definitely not gonna be Hoover/FDR but with Trump and Bernie because Trump won't be there for long enough and Bernie won't be president lol.
I dont know too much about the topic, and should probably read up about it cause it sounds interesting.
But my gut feeling is that its always the governments fault at some level. And most probably because they where not enacting the controls over trading systems the way they should have.
However, economic theory is always improving, and you cant expect the fed from the 1930's to know what we know today.