In the event they do, the third-party software adds a Google Sign In flow to their software, whereas their users can press a call-to-action for signing in with Google, which would trigger an opening of a separate Google-owned domain in a new min-browser window that the third-party software cannot access (and therefore not harvest information from). This min-window then sends the user back to the third-party software domain upon completion with an authentication token - which could be in the form of a URL query string, an HTTP method, a cookie, or even collection of arbitrary browser information for fingerprinting. The third-party site then sends that authentication token back to Google via their API, and Google sends back ONLY what that authentication token is permitted to grant access to - which would not be Google credentials.
If I'm asked to sign in with google via oauth, I never type in my password (or username!).
Now you're talking about phishing sites.
Can you clarify which kind of websites you're referring to?
It's really as easy as these companies that support Oauth incentivizing third-party devs to use them.