Google Home App Issue with SmartThings Thermostat

Hello Everyone, apologies if I posted on the wrong thread. I’m still new to this community and would be greatly appreciated if it can be posted on the right thread if this is the incorrect thread.

I am trying to use Google Home App by Adding device linked via SmartThings.
Our device in SmartThings is a thermostat device.
It is develop using SmarThings Schema connector.

This device was successfully integrated in SmartThings and we can control the modes, setpoints, and can successfully view Ambient Temperature from SmartThings App UI.

I am now trying to use Google Home App and added my SmartThings Thermostat device into the Google Home App and was added successfully.
However, our device could not successfully display the correct thermostat modes in Google Home App.
It only displays Heat mode and Cancel options, even though in SmartThings app, mode displays from [“auto”,“emergency heat”,“cool”,“heat”,“off”].

My question now is:

  1. Do any of you here made a successful attempt to link your SmartThings Schema connector-based SmartThings device in Google Home App? I asked because most of the reference that were successfully linked to Google Home App google is via SmartApp connector. I couldn’t find yet that made a successful attempt from SmartThings Schema connector-based ST device.

  2. I see an option in SmartThings App menu about Google Home App settings when browsing SmartThings App->Settings Icon->Connected Services->(MyRoomName)->Google. In the settings page, when I turn off the switch “Allow Google Assistant to access all devices, Scenes, and Routines”, I see Thermostats option that is disabled and display No device found. May I know how can I enable this options with my SmartThings Schema connector-based Device? Attached screenshot is what I see in the SmartThings App Google settings.

I erased the device name for my privacy.
Any inputs would be greatly appreciated.

Thank you.

As for the Heat mode only option, below is the screenshot:

I have this exact same issue, made a schema connector, only heating mode is available.