### 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_api2", description="this is my api")
        rest_api_id = response["id"]
        # CREATE
        domain_name = "domain2.example.com"
        client.create_domain_name(domainName=domain_name)
        root_res_id = client.get_resources(restApiId=rest_api_id)["items"][0]["id"]
        res_id = client.create_resource(
            restApiId=rest_api_id, parentId=root_res_id, pathPart="path"
        )["id"]
        client.put_method(
            restApiId=rest_api_id, resourceId=res_id, httpMethod="GET", authorizationType="NONE"
        )
        client.put_integration(
            restApiId=rest_api_id, resourceId=res_id, httpMethod="GET", type="MOCK"
        )
        depl_id = client.create_deployment(restApiId=rest_api_id)["id"]
        client.create_stage(restApiId=rest_api_id, deploymentId=depl_id, stageName="dev")
        result = client.create_base_path_mapping(
            domainName=domain_name,
            basePath="",
            restApiId=rest_api_id,
            stage="dev",
        )
        self.assertIn(result["ResponseMetadata"]["HTTPStatusCode"], [200, 201])
        base_path = "(none)"
        # LIST
        result = client.get_base_path_mappings(domainName=domain_name)
        self.assertEqual(200, result["ResponseMetadata"]["HTTPStatusCode"])