Bitcoin transactions are recorder on a public blockchain making them traceable to some extent. Although your identity isn't tied to you bitcoin wallet, advanced analytics can link wallet addresses to individuals which raises concerns for those who value privacy.
Bitcoin is pseudonymous therefore there is ways that you can make it anonymous not that the transaction wouldn’t be public but won’t be traceable to you. Just as you have said if it is not sent to an address on a platform tied to your KYC then it is safe, also there is the IP address of the user linking up addresses through the use of public nodes and not having yours, having your own full node prevents this or using Tor/vpn too. The simplest method though not to link addresses together is to prioritize the use of new address for new transactions, this ways if been utilize can keep you anonymous