iPhones have been able to do a similar thing. They don't "circle to search" but they are aware of what's on the photo. And that's done completely 100% without Google.

If you're on an Android phone that works perfectly well, look for alternatives to Google Lens. That was the precursor to Circle to Search (and it is/was available on iOS). I'm sure there are competing apps.

Of course, the one on iOS is powered by Siri... which is about to be powered by Gemini (aka, Google).

And yes, Google probably does keep the screenshots it searches, "just in case," like for legal purposes. It's probably in the TOS somewhere.