Is my privacy truly safeguarded?
Yes it is.
It's your role to ensure that you practice privacy. Nobody will do it for you.
1. Avoid centralized exchanges that ask for KYC.
2. Use Tor browser or good VPNs when using trading platforms
3. Use decentralized p2p exchanges like Bisq
4. Use change addresses. Avoid address re-use for payments
5. Use Bitcoin mixers
If the address or transaction is not linked to you (or any of your personal accounts) then privacy has been safeguarded. It doesn't matter if it's visible on the blockchain explorer or not.