Hello Mike,
It looks like using the Teams Bot for posting to GCC tenants is not available.
A person using Power Automate mentioned creating a private channel (with just you and others you want to include and use your account to post the messages instead of the Teams Bot).
May be considered more of a hack, but i created a private channel for myself, and i just have myself leaving me alerts -- though notifications are messed up because of that, so you just have to look out for the channel name to be bolded
Until it is available for GCC, this might be your only available solution.
If this is helpful please accept answer.