### 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
integration_type_orig = integration.get("type") or integration.get("integrationType") or ""
    integration_type = integration_type_orig.upper()
    uri = integration.get("uri") or integration.get("integrationUri") or ""
    try:
        path_params = extract_path_params(path=relative_path, extracted_path=resource_path)
        invocation_context.path_params = path_params
    except Exception:
        path_params = {}
    if (uri.startswith("arn:aws:apigateway:") and ":lambda:path" in uri) or uri.startswith(
        "arn:aws:lambda"
    ):
        if integration_type in ["AWS", "AWS_PROXY"]:
            func_arn = uri
            if ":lambda:path" in uri:
                func_arn = (
                    uri.split(":lambda:path")[1].split("functions/")[1].split("/invocations")[0]
                )
            invocation_context.context = get_event_request_context(invocation_context)
            invocation_context.stage_variables = helpers.get_stage_variables(invocation_context)
            request_templates = RequestTemplates()
            payload = request_templates.render(invocation_context)
            
            result = lambda_api.process_apigateway_invocation(
                func_arn,
                relative_path,
                payload,
                stage,
                api_id,
                headers,
                is_base64_encoded=invocation_context.is_data_base64_encoded,