Local traces
History, cookies, caches and session restore can persist after a browsing session unless the browser deliberately isolates or clears them.
Tracking signals
Third-party cookies, tracking query parameters and fingerprintable browser features can contribute to cross-site recognition.
Network identity
A browser-side private mode does not automatically hide the public IP. Network routing is a separate layer.
Downloads
Downloaded files leave the browser and become operating-system files. A privacy browser should clearly warn the user when a download creates a persistent artifact.