Monero itself is not KYC, sorry if I worded that poorly above.
The transactions to and from Kraken can definitely be tracked since they would have a record of the actual wallet address you sent your funds to. As for things that happen after that money hits your wallet - you’re right they wouldn’t be able to track it.
I checked the Monero subreddit just to see if my understanding of it tracked with what people who actually own it say and it looks like they agree that transferring from a KYC exchange does allow tracking for transactions coming out or into the exchange.
https://reddit.com/r/Monero/comments/ppcusq/moving_funds_bet...