### 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_
return requests.request(method, url, data=data, headers=headers, stream=True, verify=False)
    def matches(self, host, path):
        
        
        
        
        if self.base_url.netloc:
            stripped_netloc, _, port = self.base_url.netloc.rpartition(":")
            if host != self.base_url.netloc and (
                host != stripped_netloc or port not in ["80", "443"]
            ):
                return False
        
        if self.base_url.path == "/":
            if path.startswith("/"):
                return True
        path_parts = path.split("/")
        base_path_parts = self.base_url.path.split("/")
        if len(base_path_parts) > len(path_parts):
            return False
        for i, component in enumerate(base_path_parts):
            if component != path_parts[i]:
                return False
        return True
    def build_forward_url(self, host, path):