Then the possibilities I can think of are:

1. Phishing/Fake website... you're not actually logging into Kucoin, but a scam clone version that is hardcoded to use hackers address. Check the URL very carefully... perhaps try to type it out manually instead of relying on a bookmark.

2. Bad browser extension... what browser are you using? and have you looked at the settings to see what extensions/addons are running? Maybe try a different browser to see if the same thing happens.

3. Do you have tampermonkey or greasemonkey installed? If so, check to see what scripts are running... Again, try a different browser to see if the same thing happens.

4. Kucoin specific clipboard hijacker. Can't say I've heard of a clipboard malware that was specific to one site... but it might do it on other exchanges as well. Have you tried other exchanges? or just Kucoin?