### 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
result_string = b''
        while seconds is None or (time.time() - start < seconds):
            key_pressed = None
            try:
                os.set_blocking(self._stdin_fd, False)
                while key_pressed is None and (seconds is None or (time.time() - start < seconds)):
                    key_pressed = self._stdin.read(1)
                    
                    time.sleep(C.DEFAULT_INTERNAL_POLL_INTERVAL)
            finally:
                os.set_blocking(self._stdin_fd, True)
                if key_pressed is None:
                    key_pressed = b''
            if (interrupt_input is None and key_pressed == interrupt) or (interrupt_input is not None and key_pressed.lower() in interrupt_input):
                clear_line(self._stdout)
                raise AnsiblePromptInterrupt('user interrupt')
            if (complete_input is None and key_pressed in (b'\r', b'\n')) or (complete_input is not None and key_pressed.lower() in complete_input):
                clear_line(self._stdout)
                break
            elif key_pressed in backspace_sequences:
                clear_line(self._stdout)
                result_string = result_string[:-1]
                if echo:
                    self._stdout.write(result_string)
                self._stdout.flush()
            else:
                result_string += key_pressed
        return result_string
    @property
    def _stdin(self) -> t.BinaryIO | None: