I would assume that while they don't tie your search with your username (when you turn it off), they would still store it anonymously to your location, IP addre

I would assume that while they don't tie your search with your username (when you turn it off), they would still store it anonymously to your location, IP address, browser, etc. to 'improve their results using Machine Learning'. Theoretically, this could be used to identify you if all those parameters were unique to you