### Is there an existing issue for this?

- [X] I have searched the existing issues

### Current Behavior

localstack v0.12.17 released with this enhancement that downcases all headers:

> canonicalize HTTP header names in API GW Lambda events to lower-case
> https://github.com/localstack/localstack/commit/657d9fe4bd0e3c4284e6fa67aec62d265d5d9fff

This does not match what we observe in production - custom headers are not downcased. See this part of the docs on API Gateway and how it canonicalizes headers:

> API Gateway enacts the following restrictions and limitations when handling methods with either Lambda integration or HTTP integration.
> * Header names and query parameters are processed in a case-sensitive way.
> * The following table lists the headers that may be dropped, remapped, or otherwise modified when sent to your integration endpoint or sent back by your integration endpoint. In this table: 
> https://docs.aws.amazon.com/apigateway/latest/developerguide/api-gateway-known-issues.html

### Expected Behavior

I would expect that localstack follows the same canonicalization rules that API Gateway implements.

### How are you starting LocalStack?

With a docker-compose file

### Steps To Reproduce

#### How are you starting localstack (e.g., `bin/localstack` command, arguments, or `docker-compose.yml`)

    docker run localstack/localstack:0.12.17

#### Client commands (e.g., AWS SDK code snippet, or sequence of "awslocal" commands)

Used [Insomnia](https://insomnia.rest/) client to issue a POST request to an AWS Lambda function via API Gateway with custom headers. For example, `X-A-Custom-Header`. Attempt to read the custom header in your lambda function case sensitively.


### Environment

```markdown
- OS: macOS for POST request + whatever the docker container uses for localstack
- LocalStack: 0.12.17
```


### Anything else?

_No response_
apigw_client = aws_stack.create_external_boto_client("apigateway")
        s3_client = aws_stack.create_external_boto_client("s3")
        bucket_name = "test-bucket"
        object_name = "test.json"
        object_content = '{ "success": "true" }'
        object_content_type = "application/json"
        api = apigw_client.create_rest_api(name="test")
        api_id = api["id"]
        s3_client.create_bucket(Bucket=bucket_name)
        s3_client.put_object(
            Bucket=bucket_name,
            Key=object_name,
            Body=object_content,
            ContentType=object_content_type,
        )
        self.connect_api_gateway_to_s3(bucket_name, object_name, api_id, "GET")
        apigw_client.create_deployment(restApiId=api_id, stageName="test")
        url = gateway_request_url(api_id, "test", "/")
        result = requests.get(url)
        self.assertEqual(200, result.status_code)
        self.assertEqual(object_content, result.text)
        self.assertEqual(object_content_type, result.headers["content-type"])
        
        apigw_client.delete_rest_api(restApiId=api_id)
        s3_client.delete_object(Bucket=bucket_name, Key=object_name)
        s3_client.delete_bucket(Bucket=bucket_name)
    def test_api_mock_integration_response_params(self):