### Summary

If you run `ANSIBLE_LOG_PATH=test ansible localhost -m setup`, `test` is now an empty file. Before #81692 got merged, it contained log output like
```
023-11-16 08:01:52,262 p=313108 u=felix n=ansible | [WARNING]: You are running the development version of Ansible. You should only run Ansible from "devel" if you are modifying the Ansible engine, or trying out features under development.
This is a rapidly changing source of code and can become unstable at any point.

2023-11-16 08:01:52,383 p=313108 u=felix n=ansible | [WARNING]: No inventory was parsed, only implicit localhost is available

2023-11-16 08:01:53,511 p=313108 u=felix n=ansible | localhost | SUCCESS => {
    "ansible_facts": {
...
```

### Issue Type

Bug Report

### Component Name

logging

### Ansible Version

```console
latest devel branch
```


### Configuration

```console
-
```


### OS / Environment

-

### Steps to Reproduce

Run `ANSIBLE_LOG_PATH=test ansible localhost -m setup`

### Expected Results

File `test` contains log output.

### Actual Results

```console
File `test` is empty.
```


### Code of Conduct

- [X] I agree to follow the Ansible Code of Conduct
if self._final_q:
            raise NotImplementedError
        try:
            return sys.stdin.buffer
        except AttributeError:
            return None
    @property
    def _stdin_fd(self) -> int | None:
        try:
            return self._stdin.fileno()
        except (ValueError, AttributeError):
            return None
    @property
    def _stdout(self) -> t.BinaryIO:
        if self._final_q:
            raise NotImplementedError
        return sys.stdout.buffer
    @property
    def _stdout_fd(self) -> int | None:
        try:
            return self._stdout.fileno()
        except (ValueError, AttributeError):
            return None