Hello,
It sounds like you’re almost there! It seems that Google Home doesn’t fully support certain types of sensors, like template sensors, in the voice tab. However, since you mentioned that Assist does work, you might be able to use that feature to get the information you need.
Could you try using Google Assistant to ask about the state of your sensors instead? For example, you could say, “Hey Google, what is the temperature in the living room?” and see if it provides the information you’re looking for.
Without the actual code of your template entities I don’t see how anyone will be able to help you. As of now I can only guess that you have not properly configured the template sensors as measuring temperature by setting device_class to temperature and/or something is wonky with your unit_of_measurement.