### 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_templates = ResponseTemplates()
        response_templates.render(invocation_context)
        return invocation_context.response
    elif integration_type == "MOCK":
        
        invocation_context.stage_variables = helpers.get_stage_variables(invocation_context)
        invocation_context.response = requests_response({})
        response_templates = ResponseTemplates()
        response_templates.render(invocation_context)
        return invocation_context.response
    if method == "OPTIONS":
        
        return get_cors_response(headers)
    raise Exception(
        'API Gateway integration type "%s", method "%s", URI "%s" not yet implemented'
        % (integration_type, method, uri)
    )
def get_target_resource_details(invocation_context: ApiInvocationContext) -> Tuple[str, Dict]:
    """Look up and return the API GW resource (path pattern + resource dict) for the given invocation context."""
    path_map = helpers.get_rest_api_paths(
        rest_api_id=invocation_context.api_id, region_name=invocation_context.region_name
    )
    relative_path = invocation_context.invocation_path
    try:
        extracted_path, resource = get_resource_for_path(path=relative_path, path_map=path_map)
        invocation_context.resource = resource
        return extracted_path, resource
    except Exception:
        return None, None
def get_target_resource_method(invocation_context: ApiInvocationContext) -> Optional[Dict]: