if for fiat it's the central bank governor for a country that decides the local daily currency price against the other fiat currencies
This isn't even true for all fiat currencies, most countries basically let the free market decide the price and the central bank participates on this market to lower the volatility, i.e. it buys the national currency when it goes down and sells it if it grows too fast. There are still some countries that fix exchange rate, but they are a minority.