Google "detected unusual traffic" message in Safari on iPhone

Almost every time I search something on Safari in Private Browsing, I get this message and have to do a Captcha thing.

I found the cause and solution, and wanted to share it here. Would have replied to other posts, but they were all closed.

On iOS18, you need to go to Settings /Apps /Safari /Advanced and turn off the feature called Advanced Tracking and Fingerprint Print Protection.

Mine was set to Private Browsing.

After doing this, my searches started to behave normally. Hope this can help some people.