### Is there an existing issue for this?

- [X] I have searched the existing issues

### Current Behavior

Authorization headers being sent to API gateway are received on lambdas as "empty string"

### Expected Behavior

_No response_

### How are you starting LocalStack?

With a docker-compose file

### Steps To Reproduce

Run a API Gateway with lambda integration

### Environment

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


### Anything else?

_No response_
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 = helpers.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)
            except Exception as e:
                LOG.warning("Unable to convert API Gateway payload to str", e)
                raise
            
            headers = aws_stack.mock_aws_request_headers(
                service="kinesis", region_name=invocation_context.region_name
            )
            headers["X-Amz-Target"] = target
            result = common.make_http_request(
                url=config.service_url("kineses"), data=payload, headers=headers, method="POST"
            )
            
            invocation_context.response = result
            response_templates = ResponseTemplates()
            response_templates.render(invocation_context)
            return invocation_context.response
        elif "states:action/" in uri:
            return StepFunctionIntegration().invoke(invocation_context)