### 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_
integrationHttpMethod="GET",
            type="HTTP",
            uri=backend_url,
            timeoutInMillis=3000,
            contentHandling="CONVERT_TO_BINARY",
            requestParameters={"integration.request.path.id": "method.request.path.id"},
        )
        client.create_deployment(restApiId=api_id, stageName="test")
        def _test_invoke(url):
            result = requests.get(url)
            content = json.loads(to_str(result.content))
            self.assertEqual(200, result.status_code)
            self.assertRegex(
                content["headers"].get(HEADER_LOCALSTACK_REQUEST_URL),
                "http://.*localhost.*/person/123",
            )
        for use_hostname in [True, False]:
            for use_ssl in [True, False] if use_hostname else [False]:
                url = self._get_invoke_endpoint(
                    api_id,
                    stage="test",
                    path="/person/123",
                    use_hostname=use_hostname,
                    use_ssl=use_ssl,
                )
                _test_invoke(url)
        
        client.delete_rest_api(restApiId=api_id)
        proxy.stop()
    def _get_invoke_endpoint(