I have both Firefox and Chrome on my phone and I just checked and it's literally exactly the same to turn it off: on Android Chrome it is Settings > Google Services > toggle button. They're even in almost the same position in the settings menus.

I believe the linked documentation is account wide including going to google.com in Microsoft Edge and then typing into the search box on the website. It's not surprising to me that turning off behavior on across your account in any context can't be done in browser settings.