### 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_
self.assertEqual("python-requests/testing", request_context["identity"]["userAgent"])
        self.assertEqual("POST", request_context["httpMethod"])
        self.assertEqual("HTTP/1.1", request_context["protocol"])
        self.assertIn("requestTimeEpoch", request_context)
        self.assertIn("requestTime", request_context)
        self.assertIn("requestId", request_context)
        
        headers = parsed_body.get("headers") or {}
        header_names = list(headers.keys())
        self.assertIn("host", header_names)
        self.assertIn("content-length", header_names)
        self.assertIn("user-agent", header_names)
        result = requests.delete(url, data=json.dumps(data))
        self.assertEqual(204, result.status_code)
        
        body_msg = "🙀 - 参よ"
        result = requests.post(url, data=json.dumps({"return_raw_body": body_msg}))
        self.assertEqual(body_msg, to_str(result.content))
        # send 
        binary_msg = b"\xff \xaa \x11"
        result = requests.post(url, data=binary_msg)
        result_content = json.loads(to_str(result.content))
        self.assertEqual("/yCqIBE=", result_content["body"])
        self.assertEqual(True, result_content["isBase64Encoded"])
    def test_api_gateway_lambda_proxy_integration_any_method(self):
        self._test_api_gateway_lambda_proxy_integration_any_method(
            self.TEST_LAMBDA_PROXY_BACKEND_ANY_METHOD,
            self.API_PATH_LAMBDA_PROXY_BACKEND_ANY_METHOD,
        )
    def test_api_gateway_lambda_proxy_integration_any_method_with_path_param(self):