You've linked to a BTC-USDT pair. USDT is an altcoin and not fiat. That doesn't help someone buy bitcoin with fiat.
I understand that KuCoin do have their own peer-to-peer platform for buying with fiat, but it still requires some personal information, and the coins you buy are only sent to your KuCoin account, therefore they are still not in your control until you withdraw them, and KuCoin can still lock or freeze your account and demand KYC.
You don't need to care about KYC verification when trading amounts <2BTC at exchanges.
The centralized exchanges which allow trading without KYC verification (such as Binance) only allow trading between bitcoin and altcoins - they don't allow you to purchase bitcoin with fiat without KYC. And again, any centralized exchange which offers non-KYC accounts (again, such as Binance), can and frequently does lock those accounts and demand KYC anyway.
If you want to be sure of avoiding KYC then you need to use a truly decentralized platform in which your bitcoin are never in their control.