Yea I did some digging on my end and as far as I can tell I neither violated Hong Kong (where Kucoin is based) nor my local AML thresholds that would warrant reporting my transactions to authorities.
So I doubt that is what happened. For reference, the CDD threshold by HK AML regulations is $8000 for wire transfers.
The guidelines can be verified here.

If they can make a proper case that warrants enhanced due diligence, and I do have to admit, that they could in my case, they are allowed or even required to demand Identification.
But, as far as I can tell neither HK nor European AML regulations require the data KuCoin is demanding.
HK AML Identification state only:

• full name
• date of birth
• nationality
• unique identification number

My 'local' AML in addition also always requires a residential address.