### 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_
)
        
        path = path.replace("{test_param1}", "foo1")
        url = gateway_request_url(api_id=result["id"], stage_name=self.TEST_STAGE_NAME, path=path)
        data = {}
        for method in ("GET", "POST", "PUT", "PATCH", "DELETE", "OPTIONS"):
            body = json.dumps(data) if method in ("POST", "PUT", "PATCH") else None
            result = getattr(requests, method.lower())(url, data=body)
            if method != "DELETE":
                self.assertEqual(200, result.status_code)
                parsed_body = json.loads(to_str(result.content))
                self.assertEqual(method, parsed_body.get("httpMethod"))
            else:
                self.assertEqual(204, result.status_code)
    def test_apigateway_with_custom_authorization_method(self):
        apigw_client = aws_stack.create_external_boto_client("apigateway")
        # creat
        lambda_name = "apigw-lambda-%s" % short_uid()
        self.create_lambda_function(lambda_name)
        lambda_uri = aws_stack.lambda_function_arn(lambda_name)
        # creat
        api = apigw_client.create_rest_api(name="test-api", description="")
        api_id = api["id"]
        root_res_id = apigw_client.get_resources(restApiId=api_id)["items"][0]["id"]
        # creat
        authorizer = apigw_client.create_authorizer(
            restApiId=api_id,
            name="lambda_authorizer",
            type="TOKEN",
            authorizerUri="arn:aws:apigateway:us-east-1:lambda:path/ \