I'd simply like to know if when sending let's say ETH to someone from an exchange (kraken for example), the receiver can trace back your "personal" ETH key address you typically use to deposit and withdraw ETH on that exchange or just know anything that could lead to infos on your ETH public key(s) on this exchange (provided you didn't give them to begin with).
They trace your public address, not public key. It is privacy score that is affected by your deposit in and withdrawal out of exchanges. I don't know the privacy score for Ethereum transactions but blockchair.com builds the
Privacy-o-meter for Bitcoin transactions. You can see how it works for some random transactions you choose. If you want to check yours, do it with Tor connections.
(Compilation) What is the best Ethereum explorer?. Is this explorer
ETHtective.com what you are finding?
I know that on Etherscan it shows the Exchange's key (often called the name of the exchange, e.g. "Kraken 5")
It is a label or tag, not a key.
Exchanges never really specifically mentionned what information they give to the receiver but at first glance one could have guessed it's "anonymous" since it comes from the exchange's wallet and not the public key they provided to you, but if it's not the case, they should specifically say so cause some people could be deceived by this lack of informations/knowledge.
Exchange wallets or addresses are very easily to be recognized. They do many transactions in short time and with send-outs, they often proceed from one address to multiple addresses (as for batch transaction for multiple withdrawal requests from customers).
One person usually do transaction from one address to another address (or two if they use change address).