Using the CT101 and Generic Z-Wave Thermostat drivers as examples:
CT101 (works w/ Google Home)
Generic Z-Wave (does not work w/ Google home)
So nothing interesting there. If you look at the differences in data:
CT101
Generic
In the above case these are two physically different devices and the reason for that is because after I switched the Generic one to CT101 and the lastRunningMode data value was set, even after I switched it back to Generic that value was still there. Before I messed with it the value was not present like shown in the above unmodified device. I can confirm that the value is no longer being updated after switched back to Generic because when I switched the modes between heat/cool the lastRunningMode value did not change.
As for lastRunningMode not being visible to Google Home, this quote may somewhat explain how it comes into play:
