The main problems that caused the 1929 crash- rampant stock speculation,
defaults by Germany on loans due to hyperinflation, foreign markets for American goods drying up weren't run or influenced by the Fed.
Even thinking the Fed has anything vaguely to do with that presupposes monetarist theory (manipulating interest rates) which didn't really arrive until the 1950's courtesy of Milton Friedman.
What boned the Federal Reserve system from the Harding Administration on
was lax oversight and enforcement of reserve requirements for banks.