### 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_
"requestTemplates": {"application/json": "{}"},
                    }
                ],
            },
        ]
        return aws_stack.create_api_gateway(
            name=gateway_name, resources=resources, stage_name=self.TEST_STAGE_NAME
        )
    def connect_api_gateway_to_http(
        self, int_type, gateway_name, target_url, methods=None, path=None
    ):
        if methods is None:
            methods = []
        if not methods:
            methods = ["GET", "POST"]
        if not path:
            path = "/"
        resources = {}
        resource_path = path.replace("/", "")
        resources[resource_path] = []
        req_templates = (
            {"application/json": json.dumps({"foo": "bar"})} if int_type == "custom" else {}
        )
        for method in methods:
            resources[resource_path].append(
                {
                    "httpMethod": method,
                    "integrations": [
                        {
                            "type": "HTTP" if int_type == "custom" else "HTTP_PROXY",