May I suggest the below insights to your point of view, which will allow you to have a better understanding of what is happening underneath the hood ?

USDC is issued by circle.com and the underlying assets are held on US bank accounts.

BUSD, which is Binance's USD stablecoin, is actually issued by paxos.com (see https://paxos.com/busd/) and the underlying assets are held on US bank accounts .

Binance definitely has accounts at both Circle and Paxos, that allow them to mint and redeem USDC and BUSD, by depositing or (respectively) withdrawing USD to Circle's or Paxos' bank account.

In September, Binance announced that all USDC deposits made on Binance would be converted to BUSD at 1:1 (https://www.binance.com/en/support/announcement/binance-to-a...). The move was indeed an attempt to boost the adoption of BUSD, which is the third largest stablecoin with a market cap of $19B, behind USDC which is the second largest with a market cap of $43B (see https://coinmarketcap.com/view/stablecoin/).

From a practical point of view, what Binance did was redeeming the USDC (by sending them back to Circle and withdrawing USD to it's bank account) and then subsequently minting BUSD (by wiring the USD to Paxos' bank account and receiving the corresponding amount of BUSD).

Binance also allows to "seamlessly" withdraw BUSD as USDC from it's exchange to your wallet.

Now you are starting to understand what happened today.

Following negative rumours, people started to massively withdraw BUSD as USDC from Binance. Binance fullfilled to first part of those withdrawal requests from it's hot wallets containing USDC, but past a certain amount it had no USDC left and temporarily halted withdrawals of USDC. A caveat to that is that Binance only halted withdrawals of USDC on the Ethereum and Tron chains. Withdrawal of USDC to Polygon and Avalanche for example have been running smooth all day, probably because less people choose those options, so there were still funds available on Binance's hot wallets on these chains.

Once the hot wallets were depleted of USDC on Ethereum and Tron, Binance could only continue to honor the withdrawal requests by converting the BUSD it held to USDC. That conversion requires to redeem the BUSD at Paxos, receiving USD on it's bank account, sending the USD to Circle, and receiving the corresponding amount of USDC. These steps involve regular wires between banks, hence why they could not be executed before the US banks opened.

That being said, the situation is now resolved and Binance has now re-enabled withdrawals of USDC.