@Alec,
May not be that extension specifically — could be another one which is why I suggested disabling all your extensions. That being said, if you created a new profile it extensions are likely not the cause. However, if you created a new profile then it’s probably not a cookie that’s not getting deleted either, right (since the new profile would have no cookies/browsing history in it when created)?
I can log into Google/Google accounts and so can 99% of our users, so there is some issue happening beneath the surface here — it’s not that Brave “just doesn’t work with Google”.
If you want to continue helping us figure this out, I’ve reached out to the team for more input — in the interim, the next test I would suggest is try downloading the Beta build of the browser and see if you get the same behavior there. Note that this will install Beta in parallel to your current installation (no data will be deleted or overwritten).