### 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_
"uri": target_url,
                            "requestTemplates": req_templates,
                            "responseTemplates": {},
                        }
                    ],
                }
            )
        return aws_stack.create_api_gateway(
            name=gateway_name, resources=resources, stage_name=self.TEST_STAGE_NAME
        )
    @staticmethod
    def create_lambda_function(fn_name):
        testutil.create_lambda_function(
            handler_file=TEST_LAMBDA_PYTHON, libs=TEST_LAMBDA_LIBS, func_name=fn_name
        )
    def test_apigw_test_invoke_method_api(self):
        client = aws_stack.create_external_boto_client("apigateway")
        lambda_client = aws_stack.create_external_boto_client("lambda")
        # creat
        fn_name = f"test-{short_uid()}"
        testutil.create_lambda_function(
            handler_file=TEST_LAMBDA_HANDLER_JS, func_name=fn_name, runtime=LAMBDA_RUNTIME_NODEJS12X
        )
        lambda_arn_1 = aws_stack.lambda_function_arn(fn_name)
        # creat
        rest_api = client.create_rest_api(name="test", description="test")
        root_resource = client.get_resources(restApiId=rest_api["id"])
        resource = client.create_resource(
            restApiId=rest_api["id"], parentId=root_resource["items"][0]["id"], pathPart="foo"
        )