Do you remember the class-action lawsuit recently where people claimed that Google still tracks you in incognito mode - meaning that Chrome's incognito mode worked exactly as you or I would expect, but if you happen to visit sites with Google Analytics or Google Ads in a single incognito session, those products will leave cookies in that session exactly as you or I would expect?

The average person does not draw a meaningful distinction between a Google login button in the browser and a Google login button on a website. The least confusing UX actually is to avoid the situation where you log into your Google account for e.g. Gmail and then Chrome says "You're logged out."

As others have mentioned, Firefox container tabs are fantastic for solving this (I have a separate "Google" tab, so my normal browsing remains logged out), and I think those of us who care about these things owe it to the world to use Firefox.