Prevent Google Auto-sign

Hello,

I just wiped my laptop clean and reinstalled Brave for the first time.

After using Google-sites (GMail, YouTube) I realizied, that when using the Google-search-engine, I am also logged in with my Google-Account.

Before wiping my laptop it was possible for me to stay signed-in in GMail and YouTube but not the Google-search engine.

I am looking for a way that prevents this from happening. I am certain that it was not this way before the reinstall.
I saw simular requests like here, but I was not able to identify a valid solution besides switching to private browsing.
The auto-sign-in checkmark in the Brave settings also didn’t help

Do you have any suggestion on what to do?

Thanks in advance.
I apologize if my writing is confusing, since english in not my first language.