Anonymous is not the same as browsing privately. PG mentions this on top of the browser recommendation page.
If you need to browse the internet anonymously, you should use Tor instead. We make some configuration recommendations on this page, but all browsers other than Tor Browser will be traceable by somebody in some manner or another
Fingerprinting is different thing where websites try to track your browser between sessions.
You can check fingerprinting test for your browser here - https://coveryourtracks.eff.org/ >
But the results from these tests, cannot be taken as absolute conclusions about how well your browser will protect you from fingerprinting.
Fingerprinting and measures to prevent is a topic which can be researched and discussed in much more detail refer Browser fingerprinting/tracking overview