I also have no temperature displayed in Google Home.
When asking user of other products connected to Google Assistant (so without Home Assistant), they have their thermometer temperature displayed in Google Home.
So displaying temperature in Home is definitely possible now, but I am not sure why it does not work for Home Assistant.
By looking to the link given by @separac it looks like a little nuance of the way they expose temperature sensor but I am not sure.
I opened an issue on Github: Temperature sansor value not displayed in the Google Home app · Issue #92242 · home-assistant/core · GitHub
It works for me now, temperatures are shown. Not sure whether that’s due to a fix in 2023.6 or due to the new google home app.
It is the Google Home app which now provide temperatures.
Interestingly, temperature sensors are not part of climate part of the Home app but we talk about Google so we cannot understand 
I have another problem: I see both the temperature and the percentage of humidity detected by the sensor in the Google home app but if I question the Google assistant with my voice asking what temperature I have in my house, Google replies that I need a compatible thermostat. For a few days before, Google’s assistant responded correctly, telling me both the temperature and the humidity percentage, but now no longer, in fact sometimes it responds to me that the climate temperature is set at 16 degrees (which is correct because this setting is defined in my sensor which acts as the IR remote control of my old LG air conditioner).
Sorry I have wrong forum. I have Smart Life App not Home Assistant