Umm, just want to ask a question that might clarify the difference. What you’re speaking about is History, rather than Autocomplete, right?
The difference is History will show up with past searches. Whereas autocomplete will actually offer suggestions as you type. Difference between the two shown in screenshots below:
Autocompletion On:
Autocompletion Off
You see when I hit C with it turned on, that it automatically suggested community.brave.com and a bunch of other sites that start with C based on History. But when turned off, it didn’t suggest anything. But yes, recent History then showed instead.
Asking and clarifying as I think it really is two different functions. So rather than talking about autocomplete as the issue at hand, it would just be that you’d like it not to save History.
And I think only way you can do that is to use Private Window or to clear History on exit. Anything more than that would be a feature request or something.
Anyway, that’s my question and contribution. Hoping maybe helps narrow things down and point in direction of a solution.