### 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_
2, len(rs["items"])
        )  # shoul
        resource = [res for res in rs["items"] if res["path"] == "/test"][0]
        self.assertIn("GET", resource["resourceMethods"])
        
        client.delete_rest_api(restApiId=rest_api_id)
        spec_file = load_file(TEST_IMPORT_REST_API_FILE)
        rs = client.import_rest_api(body=spec_file)
        self.assertEqual(200, rs["ResponseMetadata"]["HTTPStatusCode"])
        rest_api_id = rs["id"]
        rs = client.get_resources(restApiId=rest_api_id)
        resources = rs["items"]
        self.assertEqual(3, len(resources))
        paths = [res["path"] for res in resources]
        self.assertIn("/", paths)
        self.assertIn("/pets", paths)
        self.assertIn("/pets/{petId}", paths)
        
        client.delete_rest_api(restApiId=rest_api_id)
    def test_step_function_integrations(self):
        client = aws_stack.create_external_boto_client("apigateway")
        sfn_client = aws_stack.create_external_boto_client("stepfunctions")
        lambda_client = aws_stack.create_external_boto_client("lambda")
        state_machine_name = "test"
        state_machine_def = {
            "Comment": "Hello World example",
            "StartAt": "step1",
            "States": {
                "step1": {"Type": "Task", "Resource": "__tbd__", "End": True},
            },