### 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_
"usagePlanId": usage_plan_id,
                    "keyId": api_key["id"],
                    "keyType": key_type,
                }
                client.create_usage_plan_key(**payload)
                api_keys.append(api_key["value"])
        response = requests.put(
            url,
            json.dumps({"id": "id1", "data": "foobar123"}),
        )
        # when 
        self.assertEqual(403, response.status_code)
        # check 
        for key in api_keys:
            response = requests.put(
                url,
                json.dumps({"id": "id1", "data": "foobar123"}),
                headers={"X-API-Key": key},
            )
            # when 
            self.assertEqual(200, response.status_code)
    def test_import_rest_api(self):
        rest_api_name = "restapi-%s" % short_uid()
        client = aws_stack.create_external_boto_client("apigateway")
        rest_api_id = client.create_rest_api(name=rest_api_name)["id"]
        spec_file = load_file(TEST_SWAGGER_FILE)
        rs = client.put_rest_api(restApiId=rest_api_id, body=spec_file, mode="overwrite")
        self.assertEqual(200, rs["ResponseMetadata"]["HTTPStatusCode"])
        rs = client.get_resources(restApiId=rest_api_id)
        self.assertEqual(