### 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,
        fn_name: str,
        path: str,
    ) -> None:
        test_result = self._test_api_gateway_lambda_proxy_integration_no_asserts(fn_name, path)
        data, resource, result, url, path_with_replace = test_result
        self.assertEqual(result.status_code, 203)
        self.assertEqual(result.headers.get("foo"), "bar123")
        self.assertIn("set-cookie", result.headers)
        try:
            parsed_body = json.loads(to_str(result.content))
        except json.decoder.JSONDecodeError as e:
            raise Exception(
                "Couldn't json-decode content: {}".format(to_str(result.content))
            ) from e
        self.assertEqual(parsed_body.get("return_status_code"), 203)
        self.assertDictEqual(parsed_body.get("return_headers"), {"foo": "bar123"})
        self.assertDictEqual(
            parsed_body.get("queryStringParameters"),
            {"foo": "foo", "bar": ["bar", "baz"]},
        )
        request_context = parsed_body.get("requestContext")
        source_ip = request_context["identity"].pop("sourceIp")
        self.assertTrue(re.match(r"^\d{1,3}\.\d{1,3}\.\d{1,3}\.\d{1,3}$", source_ip))
        expected_path = "/" + self.TEST_STAGE_NAME + "/lambda/foo1"
        self.assertEqual(expected_path, request_context["path"])
        self.assertIsNone(request_context.get("stageVariables"))
        self.assertEqual(TEST_AWS_ACCOUNT_ID, request_context["accountId"])
        self.assertEqual(resource.get("id"), request_context["resourceId"])
        self.assertEqual(self.TEST_STAGE_NAME, request_context["stage"])