Is it safe to save USDT and BUSD on binance for long term?
Many people have written similar responses to what I am about to write, so I hesitate to respond, but I think it is important to add some nuance to the responses.
In general, storing coin on an exchange will carry additional risk above the risk involved in storing coin on a private key that you exclusively control. Not everyone can properly secure (and backup) their private keys, and you should evaluate if you are able to properly do this or not. If this applies to you, in order for it to make sense for you to keep your coin on binance (or any other exchange), you will need to be compensated in some way for doing so, in an amount that outweighs the risks. Potential compensation may include interest payments, or the ability to quickly trade (when you plan on frequently doing so). It is up to you to decide how much compensation you need in order for this to make sense.
It is unclear to me which specific product you are using. It is possible that you are using the [ur=https://academy.binance.com/en/articles/how-to-use-binance-chain-wallet]"Binance Chain wallet"[/url], and if this is the case, it appears that Binance may have access to your private keys, at least based on the above guide. This is despite the fact that you are given a seed that can be used to recover your private keys. If this is the case, you should consider my above advice.