### 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
return self.verbose(msg, host=host, caplevel=3)
    def vvvvv(self, msg: str, host: str | None = None) -> None:
        return self.verbose(msg, host=host, caplevel=4)
    def vvvvvv(self, msg: str, host: str | None = None) -> None:
        return self.verbose(msg, host=host, caplevel=5)
    def debug(self, msg: str, host: str | None = None) -> None:
        if C.DEFAULT_DEBUG:
            if host is None:
                self.display("%6d %0.5f: %s" % (os.getpid(), time.time(), msg), color=C.COLOR_DEBUG)
            else:
                self.display("%6d %0.5f [%s]: %s" % (os.getpid(), time.time(), host, msg), color=C.COLOR_DEBUG)
    def verbose(self, msg: str, host: str | None = None, caplevel: int = 2) -> None:
        to_stderr = C.VERBOSE_TO_STDERR
        if self.verbosity > caplevel:
            if host is None:
                self.display(msg, color=C.COLOR_VERBOSE, stderr=to_stderr)
            else:
                self.display("<%s> %s" % (host, msg), color=C.COLOR_VERBOSE, stderr=to_stderr)
        elif self.log_verbosity > self.verbosity and self.log_verbosity > caplevel:
            
            if host is not None:
                msg = "<%s> %s" % (host, msg)
            self._log(msg, C.COLOR_VERBOSE, caplevel)
    def get_deprecation_message(
        self,
        msg: str,
        version: str | None = None,
        removed: bool = False,
        date: str | None = None,
        collection_name: str | None = None,