I haven't ever used the website you are talking about.
I just made a search and seems that the service you are referring to is an exchange.
Note that when you put your cryptocurrencies on an exchange, your coins are fully controlled by the exchange and there is no way to get a private key or a seed phrase.

I don't have much information about BSC network and the possibility of recovering your fund, but if there's a way, that can be done only by Coinlist.
So, the only thing you can do now is to contact their support.
Exchanges aren't usually helpful in such cases. But try your luck.