If I run the Tor Browser with onion routing disabled at home, obviously my real IP address is sent to the Web servers I'm connecting to, and Web servers and various third parties can make a decent guess that I'm the same person who's going to different sites because it's the same IP address.
Now, if I clear all my cookies and local storage, go to a friend's place, which has a different IP address, does the rest of Tor's privacy measures make sure that Web servers have no way of fingerprinting my browser as the same one I was using at home, or are there particular measures I must perform to identify as a different user? (Assume I'm browsing casually with no logins, etc.)
I assume the "New identity/circuit" functionality only applies to onion routing, so that would not be a relevant way to appear as a different user in this case because I've disabled the proxy functionality.