User management for AWS Amplify Gen2 applications

/dev Implement a user management feature that integrates with Amplify Auth and stores user profiles records in an Amazon DynamoDB table. The application is built on AWS Amplify Gen2. Here are the required changes:

1. Update the `amplify/data/resource.ts` file to define a data model for the user's profile:
- The user model should contain `id`, `username`, `email` and `displayName`, 'profileOwner'
- Data access for the user model is configured with the owner authorization strategy allowing read-only access for the owner defined in attribute `profileOwner`.

2. Create a new Amplify function resource for the post-authentication lambda function.
- Create a new directory and a resource file, `amplify/auth/post-confirmation/resource.ts`. Then, define the Function with `defineFunction`
- set arm64 architecture to use graviton processors
- set timeout to 30 seconds
- set memory to 512

3. Create the lambda function handler implementation:
- Create a new handler file `amplify/auth/post-authentication/handler.ts`
- The handler should map attributes from the cognito event source to a DynamoDB record that maps to the user model schema
- The format of the `profileOwner` attribute must be `<sub>::<username>`. 
- The user record should also contain a `createdAt` and `updatedAt` timestamp.
- The user record should be saved directly into the DynamoDB user table
- Handle errors gracefully without blocking authentication
- Use environment variables for the DynamoDB table name

4. Set the newly created Amplify function resource on the auth resource as a trigger.

5. Modify Amplify-generated post-authentication lambda resource
- Add necessary IAM permissions 
- Add necessary environment variables
- Remember that these modifications should be made in the `amplify/backend.ts` file after the `defineBackend` call. Only Lambda functions that are part of the amplify backend can be modified.