The Firebase config you're talking about are not in any way related to process environment variables that are used by the AWS SDK. While they have similar names, they are actually completely unrelated by implementation. You simply won't be able to use the Firebase tooling to create process environment variables used by AWS.
If you want to set up process env vars in Cloud Functions, you won't even be able to establish those with the Firebase tooling. You will have to make changes to environment variables in the Google Cloud console for the functions you have already deployed.
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