Yes I still get ReCaptchas using DuckDuckGo Google Search. My first search today was fine, my second wasn’t.
Weirdly on my mobile if I use the Google Search Bar widget, I never get the ReCaptcha. But whenever I use the browser I do, as well as on all other devices on the network.
I’ve deleted Browsec and Tunnelbear, I’ve deleted all extensions from my other browsers, deleted FireFox entirely, scanned all devices with MalwareBytes and deleted even the 1 false positive that I found.
I don’t want to say it’s a Brave thing, but this has only happened since I started using Brave… I don’t know what else it can be. Next step is to test while tethered to mobile as you say and also get a new IP for my Sky router and see if it happens again on either of those…