3 of 4 improved answer

Yes, in principle, under a gold standard, the central bank can produce more gold, which increases money supply. This lowers the short run interest rates. But the issue is that it can't fight the market price of gold: when the price of gold increases beyond the parity, people rush to exchange their paper currency for gold at the bank. The only way to make paper money more abundant is to procure more gold in some other way....

This is very different from what happens with fiat currency. With fiat currency, the central bank can buy bonds, or gold, but it can even just print money and give it away. ( that's called a helicopter drop, which is one way to actually do it..)

Even though in a gold standard, the central bank can increase money supply, this is different than buying bonds. This is because since money is backed by gold, it can't loose value relative to gold. In this case, it's really hard for the central bank to lower the value of money if it wants, for example, to stop a deflation.