### 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
) -> str:
        ''' used to print out a deprecation message.'''
        msg = msg.strip()
        if msg and msg[-1] not in ['!', '?', '.']:
            msg += '.'
        if collection_name == 'ansible.builtin':
            collection_name = 'ansible-core'
        if removed:
            header = '[DEPRECATED]: {0}'.format(msg)
            removal_fragment = 'This feature was removed'
            help_text = 'Please update your playbooks.'
        else:
            header = '[DEPRECATION WARNING]: {0}'.format(msg)
            removal_fragment = 'This feature will be removed'
            
            help_text = 'Deprecation warnings can be disabled by setting deprecation_warnings=False in ansible.cfg.'
        if collection_name:
            from_fragment = 'from {0}'.format(collection_name)
        else:
            from_fragment = ''
        if date:
            when = 'in a release after {0}.'.format(date)
        elif version:
            when = 'in version {0}.'.format(version)
        else:
            when = 'in a future release.'
        message_text = ' '.join(f for f in [header, removal_fragment, from_fragment, when, help_text] if f)
        return message_text
    @proxy_display
    def deprecated(