### 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_
"""Connects the root resource of an api gateway to the given object of an s3 bucket."""
        apigw_client = aws_stack.create_external_boto_client("apigateway")
        s3_uri = "arn:aws:apigateway:{}:s3:path/{}/{}".format(
            aws_stack.get_region(), bucket_name, file_name
        )
        test_role = "test-s3-role"
        role_arn = aws_stack.role_arn(role_name=test_role)
        resources = apigw_client.get_resources(restApiId=api_id)
        # using 
        root_resource_id = resources["items"][0]["id"]
        apigw_client.put_method(
            restApiId=api_id,
            resourceId=root_resource_id,
            httpMethod=method,
            authorizationType="NONE",
            apiKeyRequired=False,
            requestParameters={},
        )
        apigw_client.put_integration(
            restApiId=api_id,
            resourceId=root_resource_id,
            httpMethod=method,
            type="AWS",
            integrationHttpMethod=method,
            uri=s3_uri,
            credentials=role_arn,
        )
    def connect_api_gateway_to_kinesis(self, gateway_name, kinesis_stream):