Annoying Google signin popup

You have no control over what APIs a website developer chooses to implement in their page code. It's their website. However, you can choose to hide distracting items as Use Distraction Control in Safari to hide items on a webpage - Apple Support describes.

Which app are you talking about where Google automatically signs you in?

If you are talking about websites which prompt you to sign in using a Google account then there's nothing you can do about it. It's the website that's making it pop up. You could try pop-up blockers or you could get creative with a custom setting in a script blocking browser add-on if you want, but don't hold your breath.

That has nothing to do with Mac or macOS. It's entirely a website thing.

To eliminate it, the websites you visit would need to stop using Google as their sign in provider. Doubtful that's going to happen though.

Websites that use Google Sign in will produce the pop up if you are not signed in.