### 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_
response_templates = {
            "application/json": json.dumps(
                {
                    "TableName": "MusicCollection",
                    "Item": {"id": "$.Id", "data": "$.data"},
                }
            )
        }
        api_id = self.create_api_gateway_and_deploy(response_templates, True)
        url = gateway_request_url(api_id=api_id, stage_name="staging", path="/")
        client = aws_stack.create_external_boto_client("apigateway")
        # Creat
        usage_plan_ids = []
        for i in range(2):
            payload = {
                "name": "APIKEYTEST-PLAN-{}".format(i),
                "description": "Description",
                "quota": {"limit": 10, "period": "DAY", "offset": 0},
                "throttle": {"rateLimit": 2, "burstLimit": 1},
                "apiStages": [{"apiId": api_id, "stage": "staging"}],
                "tags": {"tag_key": "tag_value"},
            }
            usage_plan_ids.append(client.create_usage_plan(**payload)["id"])
        api_keys = []
        key_type = "API_KEY"
        # Creat
        for usage_plan_id in usage_plan_ids:
            for i in range(2):
                api_key = client.create_api_key(name="testMultipleApiKeys{}".format(i))
                payload = {