### 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
if path and (os.path.exists(path) and os.access(path, os.W_OK)) or os.access(os.path.dirname(path), os.W_OK):
        
        logging.basicConfig(filename=path, level=logging.INFO,  
                            format='%(asctime)s p=%(process)d u=%(user)s n=%(name)s | %(message)s')
        logger = logging.getLogger('ansible')
        for handler in logging.root.handlers:
            handler.addFilter(FilterBlackList(getattr(C, 'DEFAULT_LOG_FILTER', [])))
            handler.addFilter(FilterUserInjector())
    else:
        print("[WARNING]: log file at %s is not writeable and we cannot create it, aborting\n" % path, file=sys.stderr)
color_to_log_level = {C.COLOR_ERROR: logging.ERROR,
                      C.COLOR_WARN: logging.WARNING,
                      C.COLOR_OK: logging.INFO,
                      C.COLOR_SKIP: logging.WARNING,
                      C.COLOR_UNREACHABLE: logging.ERROR,
                      C.COLOR_DEBUG: logging.DEBUG,
                      C.COLOR_CHANGED: logging.INFO,
                      C.COLOR_DEPRECATE: logging.WARNING,
                      C.COLOR_VERBOSE: logging.INFO}
b_COW_PATHS = (
    b"/usr/bin/cowsay",
    b"/usr/games/cowsay",
    b"/usr/local/bin/cowsay",  
    b"/opt/local/bin/cowsay",  
)
def _synchronize_textiowrapper(tio: t.TextIO, lock: threading.RLock):
    
    
    
    def _wrap_with_lock(f, lock):