Private Browsing & Google

iPhone & iPad - in Safari, when I am browsing in Private Mode, if I try to login into a google account, say for age verification to watch a video on YouTube, I enter the correct username & password but get an error from Google saying that they could not verify and want to proceed with account recovery. There is no issue when I log in through normal mode nor if I access my Gmail for that account with the iOS email client.

I do not seem to have an issue logging into other password protected accounts in Private Mode.

Is this just an instance of Apple & Google not playing well together or am I missing something?

Thanks.