The inflation of the US currency happened much later. Roosevelt banned private holdings of monetary gold and gold certificates, incentivized gold imports and gold production which lead to the inflation. That was nearly 5 years into the depression though.
It does not when the money is not convertible to gold. Such is a fictitious gold standard.
The bank runs in the Depression were caused by inflation devaluing the value of a dollar by about half since 1914, yet was still convertible to gold. People suddenly realized they could DOUBLE THEIR MONEY by converting their paper money to gold. So they ran to the banks to do this. Of course, there wasn't enough gold to support that, and the banks collapsed. The runs did not stop until FDR made it illegal to exchange dollars for gold.
> The inflation of the US currency happened much later
Check the historical inflation figures. The dollar lost half its value 1914-29.
"It was valued at 12,500 korona, and defined as 3,800 to one kilogram of fine gold – which meant that the pengő was pegged to the gold standard, but without exchange obligation."
Which means it can be inflated at will. The US did the same thing, pegging the dollar to gold, then inflating the paper money. The result was fiscal collapse leading to the Great Depression. The fix was to make it illegal to exchange dollars for gold, making the "gold standard" a complete fiction.