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
Cited from https://powerusers.microsoft.com/t5/Building-Flows/Teams-post-a-message-from-the-Flow-Bot-in-GCC/td-p/391001/page/2
Until it is available for GCC, this might be your only available solution.
If this is helpful please accept answer.