### 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
def __init__(self, blacklist):
        self.blacklist = [logging.Filter(name) for name in blacklist]
    def filter(self, record):
        return not any(f.filter(record) for f in self.blacklist)
class FilterUserInjector(logging.Filter):
    """
    This is a filter which injects the current user as the 'user' attribute on each record. We need to add this filter
    to all logger handlers so that 3rd party libraries won't print an exception due to user not being defined.
    """
    try:
        username = getpass.getuser()
    except KeyError:
        
        username = 'uid=%s' % os.getuid()
    def filter(self, record):
        record.user = FilterUserInjector.username
        return True
logger = None
if getattr(C, 'DEFAULT_LOG_PATH'):
    path = C.DEFAULT_LOG_PATH