### 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
import os
import random
import subprocess
import sys
import termios
import textwrap
import threading
import time
import tty
import typing as t
from functools import wraps
from struct import unpack, pack
from ansible import constants as C
from ansible.errors import AnsibleError, AnsibleAssertionError, AnsiblePromptInterrupt, AnsiblePromptNoninteractive
from ansible.module_utils.common.text.converters import to_bytes, to_text
from ansible.module_utils.six import text_type
from ansible.utils.color import stringc
from ansible.utils.multiprocessing import context as multiprocessing_context
from ansible.utils.singleton import Singleton
from ansible.utils.unsafe_proxy import wrap_var
if t.TYPE_CHECKING:
    
    from ansible.executor.task_queue_manager import FinalQueue
_LIBC = ctypes.cdll.LoadLibrary(ctypes.util.find_library('c'))
_LIBC.wcwidth.argtypes = (ctypes.c_wchar,)
_LIBC.wcswidth.argtypes = (ctypes.c_wchar_p, ctypes.c_int)
_MAX_INT = 2 ** (ctypes.sizeof(ctypes.c_int) * 8 - 1) - 1
MOVE_TO_BOL = b'\r'
CLEAR_TO_EOL = b'\x1b[K'
def get_text_width(text: str) -> int: