What do you mean by their own currency? They still issued USD, which was the only legal currency.
As I recall, they issued the paper version of stablecoins: they were denominated in units of US dollars, but they weren’t government money, and they traded at floating values, typically (aside from many other factors influencing value) declining in value with distance from the issuing bank.
When the Fed lost all credibility with exchanging their banknotes for gold, we had the Great Depression. FDR then defaulted on the gold bonds, basically stealing from the good citizens who had trusted the government.
This was not a cause of the Great Depression. (You are correct on the default, however.)
I mean exactly that. They issued banknotes (that's why paper money is sometimes called banknotes). The banknotes were denoted in dollars, like bank checks today.
Here's an article with some pictures:
https://thismatter.com/money/banking/history/free-banking-na...