Apologies if this is a stupid question, but I want to understand. I have Proton VPN plus, and I’m in the process of removing my Google accounts from my computer—it will take a bit of time. But I’m wondering: if the use of the VPN means that Google search engine isn’t able to know it’s me running certain searches (and thus continue to compile information about me), is there a point switching to a private search engine? Is everything pointless until my Google account is totally removed from my computer?
Please help me understand 
A VPN does not help you a lot in regards of privacy when it comes to this topic. There is much more Google can use to track you. Just read about tracking, fingerprinting………
The vpn hides your actual ip address. But there are more ways for google to track you. Use a separate browser — where you have never signed in into any Google service (gmail, YouTube etc) — to use google search, after, of course, having changed your ip by connecting to some other vpn server.
Yes, Google will still be able to collect information about you with a VPN enabled. Even if you logout.
By enabling a VPN you’re only remove one of the many things sites can track that can help them identify you. Your IP address.
A VPN is not really a good tool against being tracked by the sites you are visiting. A VPNs purpose is to hide your traffic from outsiders(people that is not you or the sites you are visiting) and to hide your IP-address/where you connect from.
Using a different search engine or using a privacy hardened browser would help you in this scenario.
