### 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
stdout.write(b'\x1b[%s' % MOVE_TO_BOL)
    stdout.write(b'\x1b[%s' % CLEAR_TO_EOL)
def setup_prompt(stdin_fd: int, stdout_fd: int, seconds: int, echo: bool) -> None:
    setraw(stdin_fd)
    
    
    if os.isatty(stdout_fd):
        setraw(stdout_fd)
    if echo:
        new_settings = termios.tcgetattr(stdin_fd)
        new_settings[3] = new_settings[3] | termios.ECHO
        termios.tcsetattr(stdin_fd, termios.TCSANOW, new_settings)
def setupterm() -> None:
    
    try:
        curses.setupterm()
    except (curses.error, TypeError, io.UnsupportedOperation):
        global HAS_CURSES
        HAS_CURSES = False
    else:
        global MOVE_TO_BOL
        global CLEAR_TO_EOL
        
        MOVE_TO_BOL = curses.tigetstr('cr') or MOVE_TO_BOL
        CLEAR_TO_EOL = curses.tigetstr('el') or CLEAR_TO_EOL
class Display(metaclass=Singleton):
    def __init__(self, verbosity: int = 0) -> None: