If I remember correctly… Google Home can control light bulbs, plugs, on/off switches, dimmers, and thermostats from ST. Others will explain using virtual switches and Routines between the two systems. 
The integration is one way → from ST to Google. Google speakers would not be exposed to ST. Unsure what Matter will bring to the table at some point.
A community developer has been working on an Edge driver for Chromecast so you can check it out: https://community.smartthings.com/t/release-cast-web-v1-2-1-chromecast-integration-edge-driver-discussion-begins-in-post-1668/88038/1696