It's asking to sign in on a browser instead of showing on Google App

If it's asking to sign in to your account even though you're already logged in to your browser, this is probably because of the default browser setting on the phone.

Here's an example:

Even though the Google Chrome app is being used, the phone's default browser is still Safari, so regardless of the link you'll be opening, your phone will always use Safari to view the link or page you're trying to access. Changing this default browser app should resolve this issue.