What private mode actually drops
Cookies, local storage, and session data for that window go away when it closes. History for that session is not kept in the normal profile.
That is useful. It is a storage boundary.
What stays on the device
Canvas pixels, WebGL renderer strings, audio output, screen size, CPU thread count, and the time zone are properties of the browser and the machine.
Run it on the fingerprint test. Compare a normal window and a private window if you want to see the overlap.
Where it still helps
It stops a site from reading the cookies it set last week in the normal profile. It does not stop a script from measuring the screen.
Global Privacy Control is a separate preference. GPC is not a fingerprint blocker.
Common questions
Should I use private mode anyway?
Yes, when you want a session that does not keep site storage. Just do not treat it as anonymity.
Does private mode change my IP?
No. The network path is the same unless you also change the network.