Google prompt not showing to iphone

I cant sign in my gmail on iphone since I cant find the way to get google prompt to youtube account and I cannot add more account to youtube just particularly one gmail account. I dont know what to do to get a google prompt on my iphone. my IOS is up todate with recent version.

its really painful and looks like I cant log in my gmail over iphone forever ( yes I cant still log on email over laptop with window hello verification.