### 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
or os.getpgrp() != os.tcgetpgrp(self._stdin_fd)
        ):
            raise AnsiblePromptNoninteractive('stdin is not interactive')
        
        
        
        
        
        
        
        
        
        self.display(msg)
        result = b''
        with self._lock:
            original_stdin_settings = termios.tcgetattr(self._stdin_fd)
            try:
                setup_prompt(self._stdin_fd, self._stdout_fd, seconds, not private)
                
                
                termios.tcflush(self._stdin, termios.TCIFLUSH)
                
                return self._read_non_blocking_stdin(echo=not private, seconds=seconds, interrupt_input=interrupt_input, complete_input=complete_input)
            finally:
                
                termios.tcsetattr(self._stdin_fd, termios.TCSADRAIN, original_stdin_settings)
    def _read_non_blocking_stdin(