Hi @LocoFG - Sorry to hear about that. I think that you might need to physically turn your Google TV off using the remote instead of just turning the TV itself off. That should hopefully turn the time limit feature off/put on pause.
Hope this helps!
Thanks for the help here, MrVacca.
LocoFG, I'm sorry to hear that you're having an issue with your Chromecast with Google TV. The screen time should not be used up when the TV is turned off. Let's sort this out.
Could you please go to the kid's profile settings and go to screen time and check if the correct time is set? If it has the correct scheduled limit time, please try to reset the time and choose again your desired limit time. See more information here.
If the issue persists, try the following steps below: