Can anyone tell me how will centralized know that the funds came from a gambling site? I'm only seeing threads before that someone claimed their account got frozen because funds came from a gambling site but no proof that the site itself tells their users that's the exact reason. Coinbase for example but not seeing cases like that in Binance. I think there is another reason why their account got frozen and not because the money was coming from a gambling site.
Furthermore, if OP is really worried, then an extra step of using a non-custodial wallet is necessary.
If funds came from any gambling site then there might have mentioned the sites name as several exchanges name also shown. If few sites, or few times it cant show the name of the site then there is a probable number of the wallets of a gambling site they may count.It might be something like the provided image below:

From your image, we can see that some providers, whether it is gambling sites or exchanges, still allow their users to deposit or withdraw the funds. But we do not know what will happen in the future as when the government knows about that, they can force the exchanges in their jurisdictions to give the reports about their members and check the account.
If their country prohibits gambling, the government will warn the user not to play gambling or use the exchange to deposit or withdraw from the exchange to the gambling or vice versa.