### 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_
data["return_is_base_64_encoded"] = True
            data["return_raw_body"] = base64.b64encode(content).decode("utf8")
        test_result = self._test_api_gateway_lambda_proxy_integration_no_asserts(
            self.TEST_LAMBDA_PROXY_BACKEND_WITH_IS_BASE64,
            self.API_PATH_LAMBDA_PROXY_BACKEND_WITH_IS_BASE64,
            data_mutator_fn=_mutate_data,
        )
        
        self.assertEqual(test_result.result.status_code, 203)
        self.assertEqual(test_result.result.content, content)
    def _test_api_gateway_lambda_proxy_integration_no_asserts(
        self,
        fn_name: str,
        path: str,
        data_mutator_fn: Optional[Callable] = None,
    ) -> ApiGatewayLambdaProxyIntegrationTestResult:
        """
        Perform the setup needed to do a POST against a Lambda Proxy Integration;
        then execute the POST.
        :param data_mutator_fn: a Callable[[Dict], None] that lets us mutate the
          data dictionary before sending it off to the lambda.
        """
        self.create_lambda_function(fn_name)
        
        lambda_uri = aws_stack.lambda_function_arn(fn_name)
        invocation_uri = "arn:aws:apigateway:%s:lambda:path/2015-03-31/functions/%s/invocations"
        target_uri = invocation_uri % (aws_stack.get_region(), lambda_uri)