I just installed my first ecobee yesterday, paired it with my google home ecosystem this morning, and found the same issue. Luckily, I found this information on reddit before wasting too much time troubleshooting:
"Fatima from ecobee here. We've received reports that ecobee Smart Thermostats and Switch+ are appearing as "offline" in the Google Home app, making them unresponsive to control within the Google Home app. However, control of ecobee Smart Thermostats and Switch+ through Google Assistant voice commands should remain unaffected. Our team is investigating. In the meantime, you can continue using the ecobee app, Google Assistant, other third-party apps, or the devices themselves to control and adjust. Thanks for your patience as we work on resolving this issue." Ecobee has a status page on their website to update progress on this (I'm a new user to this forum so I'm not sure if I can link to another site). This issue was reported on Feb 23 and so far is unresolved.
