IOS 18 and CAPTCHA

Unfortunately, that’s a question for Google. It usually means that Google is not “remembering” that you connected previously. This can happen if you are in the habit of deleting cookies, if you aren’t logged in to your Google account, if you didn’t check the “keep me logged in” box, or if you are connected through VPN.

CAPTCHA is only and totally implemented by the website. It has nothing to do with the device you're running your web browser on. Why you're getting CAPTCHA requirements when you use a Google search I can't say since I can't see how and what you're searching. If you're signed into a Google account, perhaps it has something to do with that. You would need to take that up with Google.

Otherwise, you can change your search engine to something other than Google: Settings -> Apps -> Safari -> Search Engine - and see if that avoids that hassle.

Regards.