### 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
try:
            
            _synchronize_textiowrapper(sys.stdout, self._lock)
            _synchronize_textiowrapper(sys.stderr, self._lock)
        except Exception as ex:
            self.warning(f"failed to patch stdout/stderr for fork-safety: {ex}")
        codecs.register_error('_replacing_warning_handler', self._replacing_warning_handler)
        try:
            sys.stdout.reconfigure(errors='_replacing_warning_handler')
            sys.stderr.reconfigure(errors='_replacing_warning_handler')
        except Exception as ex:
            self.warning(f"failed to reconfigure stdout/stderr with custom encoding error handler: {ex}")
        self.setup_curses = False
    def _replacing_warning_handler(self, exception: UnicodeError) -> tuple[str | bytes, int]:
        
        
        self.deprecated(
            'Non UTF-8 encoded data replaced with "?" while displaying text to stdout/stderr, this is temporary and will become an error',
            version='2.18',
        )
        return '?', exception.end
    def set_queue(self, queue: FinalQueue) -> None:
        """Set the _final_q on Display, so that we know to proxy display over the queue
        instead of directly writing to stdout/stderr from forks
        This is only needed in ansible.executor.process.worker:WorkerProcess._run
        """
        if multiprocessing_context.parent_process() is None:
            raise RuntimeError('queue cannot be set in parent process')
        self._final_q = queue
    def set_cowsay_info(self) -> None: