Private tabs do nothing for the backend, your ISP, browser, search engine, and any sites you visit, can still see everything you do. All private tabs do is they don't save history or cookies on your frontend.

VPN hides your data from your ISP, but there are still workarounds. Multi-hop can make you harder to triangulate though.

You still need to use a privacy-centric browser and search engine or else the ones you use can still send information about you back to their servers where they can build a profile on you. They won't have your real IP address as long as you never connect without a VPN, but any little data they collect on you can be collated with the rest to profile you and potentially identify you.

Even with browsers like firefox or waterfox, you still need to enable all of the security settings or else there are gaps that can be exploited. HTTPS-only mode, DNS over HTTPS, anti-tracking extensions, etc...

Even then, I wouldn't be surprised if there's an unseen gap somewhere. But it's a lot better than using google and microsoft and no vpn.