A site can also use your IP address, request headers, device characteristics, pixels, link parameters, local storage, or activity tied to a signed-in account. It can keep records on its own servers after you clear local cookies.
The W3C's fingerprinting guidance explains that a fingerprint can correlate visits across sessions and sites even when cookie rules prevent sharing. Neither clearing cookies nor using a VPN necessarily prevents that correlation.
Cookie blocking still removes a common tracking route. Treat it as one privacy layer, alongside tracker blocking, anti-fingerprinting protections, careful site permissions, and account-level data controls.