As of two weeks ago my locked down Firefox profile gets hit with captchas on every visit to Google search. DDG has also gone to shit with captchas and stupid low cache lifetime because I use their non-javascript site. I'm giving Bing a test run before making the leap to Kagi.
We (at DuckDuckGo) shouldn’t have a lot of captchas and when we do (intended to keep away non-human traffic) they are completely anonymous, self-hosted, and not related to any AI or other machine learning. As such, I’d love to figure out why you are getting ensnared in them when you aren’t supposed to. If you want to reach out via email (see my profile) I will look into it.
Try also Startpage, it doesn't give me any captchas even though I am a career criminal: guilty of adblocking under Firefox influence, while commiting a VPN. They also have a nice Anonymous view.
You might want to try Mullvad Leta, it's what i use for this issue. I would try Kagi if it could be used privately but i suppose it still requires an account and has no way to pay privately
