https://fingerprintjs.com/demo shows that Tor can still be fingerprinted and uniquely identified across IP addresses. Your Javascript (navigator) user-agent and timezone are some of the dead giveaways as they leak the true values.
There's a "new Tor circuit for this site" button in the Tor Browser, but it's for circumventing dumb WAFs who've blacklisted a Tor exit node's IP. It's not for OPSEC.
> Javascript
Nobody who cares about doing anything secretive is using Tor with Javascript enabled. (Fun fact: most of the "dark web" stuff operates using early-2000s-era phpBB forum tech, which works perfectly fine without JS.)
Download Tor https://www.torproject.org/download/
Go to your site, and see if you think it works - https://fingerprintjs.com/demo
(Also notice how Tor changes the screen size everytime you open it)