### 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_
client = aws_stack.create_external_boto_client("apigateway")
        response = client.create_rest_api(name="my_api", description="this is my api")
        rest_api_id = response["id"]
        dummy_rest_api_id = "_non_existing_"
        _name = "testModel"
        description = "test "
        content_type = "application/json"
        # add a 
        client.create_(
            restApiId=rest_api_id,
            name=_name,
            description=description,
            contentType=content_type,
        )
        # get m
        result = client.get_(restApiId=rest_api_id, Name=_name)
        self.assertEqual(_name, result["name"])
        self.assertEqual(description, result["description"])
        try:
            client.get_(restApiId=dummy_rest_api_id, Name=_name)
            self.fail("This call should not be successful as the  is not created.")
        except ClientError as e:
            self.assertEqual("NotFoundException", e.response["Error"]["Code"])
            self.assertEqual("Invalid Rest API Id specified", e.response["Error"]["Message"])
    def test_get__with_invalid_name(self):