support passing Amplify app ID to a Function (similar to `ENV`)

### Amplify CLI Version

10.8.1

### Question

The lambda function in the backed of my amplify app needs to know the amplify app id to be able to make requests to add subdomains to the app. In the cloudformation template of the lambda function, I do not see any way to pass the amplify app id. There are a few references some of which uses SSM but none is clear. I need to set the amplify app id in the environment variables of my lambda function.

Start with the Lambda function's CloudFormation template and the existing path used to pass ENV values into functions. Check how the Amplify app ID is represented elsewhere, including the referenced SSM approach, and verify the deployed function receives the value as an environment variable.

Written by the indexing model from the issue text.