Your browser has a fingerprint
Fonts, screen, and canvas. Clearing cookies does not make you a stranger.
Clearing cookies does not make you a stranger. A browser has a shape: fonts, screen, time zone, GPU, how it draws a canvas, which features it admits. Taken together, that shape is often unique enough to recognize you again. That is a fingerprint. It does not have your name. Combined with an account, it might as well.
Why sites bother
Ads want a stable ID without a third party cookie, which browsers have been killing off. Fraud teams want to know if this login looks like the same laptop as last week. Both groups buy the same kind of script. You see a page. The script measures the room.
Private windows help against cookies. They help less against fingerprints, because the hardware did not change. A VPN changes the IP. It does not change the font list. Tor Browser tries to look like other Tor users on purpose. Ordinary Chrome on a gaming PC does not.
What you can actually do
You will not vanish. You can get noisier to track. Fewer extensions (some of them make you more unique). A common browser, not a rare one. Blocking third party scripts where you can live with the breakage. Not logging into the same shopping account you use for mail if you care about that joining-up.
Fingerprint blocking that lies about every value can make you stand out as “the person with the blocker.” Sometimes the boring default is the smaller target.
The honest limit
If you signed in, the site knows you. The fingerprint is for the visits before and after that. Treat it as a reason not to expect cookies-off to mean invisible. The IP this site shows is one label. The browser is another. You walk around with both.