Where does the fiat go?

When a person purchases crypto with fiat on an exchange what happens to the fiat the crypto was purchased with?

Does it go to a bank?
Does it go into the blockchain?
Does it go to the developer?

I’m guessing you’re referring to Centralised Exchanges as that is the only way to go from fiat to crypto (apart from P2P, brokerages & Crypto ATMs).
When you purchase crypto on an exchange, your fiat gets put into the fiat liquidity pool of that exchange. No money goes to the bank or to the devs, the funds stay inside the exchange.
When you go and sell crypto through an exchange, you’re basically just giving to the crypto liquidity pool of that exchange and taking from the fiat liquidity pool.
The exchange does take a transaction fee for any transaction done on their exchange, which is basically their earnings.

(A question that I had while researching a bit: How are devs incentivized to build on the network?
Answer: They get a part of the whole token supply at the start, which gets unlocked over time.)

Hopefully this explanation isn’t too confusing.

If you want some more info these are the articles I looked at: