I appreciate that Google allows me to turn their data collection off, though I still avoid Google services where possible. I hope that this page tells the truth.
Google allows you to disassociate the data they collect from you from your account. That neither turns off data collection nor guarantees that it's impossible to associate your name with an activity stream.
It appears that their interface does not tell the truth. My YouTube search history is off, but the YouTube history is still displaying on that page, so they are still collecting and storing the info.
I found the same about YT history. None of the videos that I view on the laptop are shown in the history, only videos viewed on mobile.
I think it's because I block ip addresses, that track your data, on the laptop.