IIRC Google Home doesn't support input (Shelly Button1, Shelly I3) devices.. That's a limitation by Google, not a Shelly problem..
If that would be true (how can this statement be verified?) then that would be very disappointing, since Shelly promotes the fact that it works with Google Home and mentions no limitations whatsoever.
[edit] It should work, according the Shelly website: "..All Shelly devices are 100% compatible with Amazon Echo and Google Home.." See: https://shelly.cloud/support/compatibility/