### 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_
# apigw
        resps = [
            {
                "statusCode": "204",
                "httpMethod": "OPTIONS",
                "responseParameters": {
                    "method.response.header.Access-Control-Allow-Methods": "'POST,OPTIONS'",
                    "method.response.header.Vary": "'Origin'",
                },
            }
        ]
        api_id = self.create_api_gateway_and_deploy(
            integration_type="MOCK", integration_responses=resps
        )
        url = gateway_request_url(api_id=api_id, stage_name=self.TEST_STAGE_NAME, path="/")
        result = requests.options(url)
        self.assertLess(result.status_code, 400)
        self.assertEqual("Origin", result.headers.get("vary"))
        self.assertEqual("POST,OPTIONS", result.headers.get("Access-Control-Allow-Methods"))
    def test_api_gateway_update_resource_path_part(self):