It’s a little complicated.
The official integration only controls switches, thermostats, and bulbs. The echo integration is the same, except it can also do some routines.
https://support.smartthings.com/hc/en-us/articles/214609826-Google-Home-SmartThings-FAQ
Using a Virtual Switch
Fortunately, SmartThings allows you to create “virtual switches.” This will look just like a regular physical switch to Google home, but it exists only as a software entry in your account.
Once you have created the virtual switch, it shows up on your list of devices and there is already a smartapp from the marketplace to have that virtual switch turn on a routine or you could use that virtual switch to start a smart app or trigger another smartthings controlled device. So that’s how people usually handle door locks and some other integrations.
Alternatively, you may be able to use the IFTTT channel. This allows you to set any custom phrase you like in google home and use it as the “if” and any device in the smartthings IFTTT channel as the “that.” notice that The SmartThings device that you select could again be a virtual switch to trigger a routine, smart lighting automation, or other smart app.
So between these two options, you could probably get google home to do most of what you want.
Specifics
As far as the two specific devices you asked about, is there already a SmartThings integration with the thermostat? If so, it will just work through the regular SmartThings/google home integration, because thermostats are included.
I don’t remember what works in MyQ light or not, you could ask in that thread.
So basically, if setting up a virtual switch would get it to work with echo, then it will also get it to work with google home.