### 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 = json.dumps({"data": 123})
        result = requests.post(url, data=data)
        self.assertEqual(200, result.status_code)
        expected = custom_result if int_type == "custom" else data
        self.assertEqual(expected, json.loads(to_str(result.content))["data"])
        
        data = "test=123"
        ctype = "application/x-www-form-urlencoded"
        result = requests.post(url, data=data, headers={"content-type": ctype})
        self.assertEqual(200, result.status_code)
        content = json.loads(to_str(result.content))
        headers = CaseInsensitiveDict(content["headers"])
        expected = custom_result if int_type == "custom" else data
        self.assertEqual(expected, content["data"])
        self.assertEqual(ctype, headers["content-type"])
        
        proxy.stop()
    def test_api_gateway_lambda_proxy_integration(self):
        self._test_api_gateway_lambda_proxy_integration(
            self.TEST_LAMBDA_PROXY_BACKEND, self.API_PATH_LAMBDA_PROXY_BACKEND
        )
    def test_api_gateway_lambda_proxy_integration_with_path_param(self):
        self._test_api_gateway_lambda_proxy_integration(
            self.TEST_LAMBDA_PROXY_BACKEND_WITH_PATH_PARAM,
            self.API_PATH_LAMBDA_PROXY_BACKEND_WITH_PATH_PARAM,
        )
    def test_api_gateway_lambda_proxy_integration_with_is_base_64_encoded(self):
        
        content = b"hello, please base64 encode me"
        def _mutate_data(data) -> None: