I’ll caveat that private mode does erase cookies after the session; it does not stop all tracking. Logged into a site in private mode? Guess what, it still tracks you. Use Facebook or google services for example, they do their tracking by your login and it doesn’t matter how private your browser session is.
Your employer, likewise, can see what sites you visit (*) regardless of whether you are in browser private mode.
Think of “private mode” as “private from others that use the same PC”, but not “private from the sites I use”.
VPNs are a similar story. They can mask your IP address, but that’s meaningless if you’re logged in somewhere. Also, most will respond to a subpoena.
I see the use of VPNs to secure access to corporate networks (though, with cloud apps, that’s less and les a thing) and I’ve seen them used to bypass region-locks on copyright - stream some English footie from the US. How naughtie
Unless I’m concerned about being tracked by a nation state (certain activists and journalists), I’m not sure what a VPN gains me privacy-wise - and even then, it’s only one layer of defense, and nation states can and do track people even through something like ToR.
(*) Subject to local privacy laws - much more so in the US than the EU