### 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_
result = testutil.connect_api_gateway_to_http_with_lambda_proxy(
            "test_gateway2", target_uri, path=path, stage_name=self.TEST_STAGE_NAME
        )
        api_id = result["id"]
        path_map = get_rest_api_paths(api_id)
        _, resource = get_resource_for_path(path, path_map)
        
        path_with_replace = path.replace("{test_param1}", "foo1")
        path_with_params = path_with_replace + "?foo=foo&bar=bar&bar=baz"
        url = gateway_request_url(
            api_id=api_id, stage_name=self.TEST_STAGE_NAME, path=path_with_params
        )
        
        data = {"return_status_code": 203, "return_headers": {"foo": "bar123"}}
        if data_mutator_fn:
            assert callable(data_mutator_fn)
            data_mutator_fn(data)
        result = requests.post(
            url,
            data=json.dumps(data),
            headers={"User-Agent": "python-requests/testing"},
        )
        return ApiGatewayLambdaProxyIntegrationTestResult(
            data=data,
            resource=resource,
            result=result,
            url=url,
            path_with_replace=path_with_replace,
        )
    def _test_api_gateway_lambda_proxy_integration(