So, what will happen if what you did is that before sending to Binance is you have your own personal wallet in the middle before you send the funds to Binance?
Like 3rd party wallet -> Your personal wallet -> Binance,
Could Binance still able to find out about the "mixer" thing you said that could be the reason of restricting your account?
I think it is possible for an account restriction for asking proof of fund or even account termination after all.
Best practice is don't interact your fund with mixers, but if it is your payment from companies or someone else, you can not know what they did with their funds before sending your payment.
Receiving payments in your non custodial wallets, and if you are careful and can afford to pay transaction fees, you can move it to one or two more wallets (non custodial wallets of yours), before sending it to your CEX account.
It costs you more on chain transaction fee but if you can afford to pay it, you will have less risk.