How to add Gmail account to iPhone manually (without selecting Gmail)

I was not able to add a Google hosted email account to my iPhone Mail manually - it forced me to use the Gmail option. Now, I constantly get Google log-in pop-ups when I use Safari. I would like to stop these pop-ups. Is there a way to get Mail to accept the Google hosted email account without linking/adding Google? Would this stop the pop-ups? Is there another way to stop the pop-ups, leaving the email as is?

I found another post from a couple of years ago that said to log in to the Google account and turn off a sign-in setting - the suggested setting does not exist, that I can find, in the Google account.