Extra verification comes in handy if you and someone else use the same computer, or if you leave your phone or tablet unlocked. However it still requires the use of your Google account sign-in and does not protect your data with the use of an additional password. If you want to prevent Google from keeping your account history, go to Activity Controls and delete what detailed history is stored.
You can make your Google activity history safer by requiring extra verification to open My Activity
You can also change some settings to prevent Google from collecting your history. As Google says, “Your Web & App Activity includes the things you do on Google services, like Maps, Search, and Play. It can also include things you do on sites, apps, and devices that use Google services or your voice and audio recordings. The activity you keep is used to give you more personalized experiences, like faster searches and more helpful app and content recommendations.”
