### 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_
}
        # creat
        fn_name = "test-stepfunctions-apigw"
        testutil.create_lambda_function(
            handler_file=TEST_LAMBDA_ECHO_FILE,
            func_name=fn_name,
            runtime=LAMBDA_RUNTIME_PYTHON36,
        )
        role_arn = aws_stack.role_arn("sfn_role")
        # creat
        definition = clone(state_machine_def)
        lambda_arn_1 = aws_stack.lambda_function_arn(fn_name)
        definition["States"]["step1"]["Resource"] = lambda_arn_1
        definition = json.dumps(definition)
        # creat
        result = sfn_client.create_state_machine(
            name=state_machine_name, definition=definition, roleArn=role_arn
        )
        sm_arn = result["stateMachineArn"]
        # creat
        rest_api = client.create_rest_api(name="test", description="test")
        resources = client.get_resources(restApiId=rest_api["id"])
        root_resource_id = resources["items"][0]["id"]
        client.put_method(
            restApiId=rest_api["id"],
            resourceId=root_resource_id,
            httpMethod="POST",
            authorizationType="NONE",
        )
        def _prepare_method_integration(