it’s definitely more pro-privacy than Brave or FireFox. I’ve never had to jump through a captcha to use Google in those browsers.

You have this backwards. Google showing you captchas is basically them saying they can’t match your browser to any know (shadow) profile they have already stored. So they aren’t sure you are a human and if so which one specifically. Getting harassed with a captcha is essentially like a badge of honour for your browsers privacy settings.