Google Play yes, Google TV no. Those are separate things.
Google Play is Google's billing platform. Google TV is their subscription service and app.
If you subscribed through Google Play, then you log in with your Google account and it should enable the subscription and access to Apple TV+ content.
Google Tv is a different service, and while it may also be using your Google account it should have no real ties to the Apple TV subscription. The subscription will just appear in the Google TV App.
While your Google TV subscription may require some action, this is probably not related to the Apple TV subscription is what I'm trying to say.
If you can successfully play any episode from any show in the Apple TV+ catalog, then your subscription is working fine.
Otherwise:
https://support.google.com/googleplay/answer/9818348?hl=en&co=GENIE.Platform%3DAndroid
And contact Google Support for more help with their platform.