Well Binance claims the recepient still can find and use the funds but dont want to tell me, because they'd rather keep the funds without giving the product/service they are selling.
Well if it's Binance, then there's no problem here at all.
Firstly, USDC and USDT are ERC-20 and Binance wallet for ERC-20 compatible wallet are always the same including that of ETH.
Secondly, you should scan both wallet on etherscan.io to confirm if it's same funds that's there. Also check deposit history.
You shouldn't panic and you should talk to a customer service.