### Is there an existing issue for this?

- [X] I have searched the existing issues

### Current Behavior

We are using the `Authorization` header for routing purposes

```
 "authorization: AWS4-HMAC-SHA256 <...>"
```

https://github.com/localstack/localstack/issues/5770

### Expected Behavior

Use a custom header to avoid causing confusion with backend integrations

### How are you starting LocalStack?

With a `docker run` command

### Steps To Reproduce

Run a custom HTTP integration without authorisation

### Environment

```markdown
- OS: 
- LocalStack:
```


### Anything else?

No
response._content = body_bytes
                except Exception as e:
                    LOG.warning("Couldn't set Lambda response content: %s", e)
                    response._content = "{}"
                update_content_length(response)
                response.multi_value_headers = parsed_result.get("multiValueHeaders") or {}
            
            invocation_context.response = response
            response_templates = ResponseTemplates()
            response_templates.render(invocation_context)
            invocation_context.response.headers["Content-Length"] = str(len(response.content or ""))
            return invocation_context.response
        raise Exception(
            f'API Gateway integration type "{integration_type}", action "{uri}", method "{method}"'
        )
    elif integration_type == "AWS":
        if "kinesis:action/" in uri:
            if uri.endswith("kinesis:action/PutRecord"):
                target = kinesis_listener.ACTION_PUT_RECORD
            elif uri.endswith("kinesis:action/PutRecords"):
                target = kinesis_listener.ACTION_PUT_RECORDS
            elif uri.endswith("kinesis:action/ListStreams"):
                target = kinesis_listener.ACTION_LIST_STREAMS
            else:
                LOG.info(
                    f"Unexpected API Gateway integration URI '{uri}' for integration type {integration_type}",
                )
                target = ""
            try:
                invocation_context.context = get_event_request_context(invocation_context)