### Apache Airflow Provider(s)

amazon

### Versions of Apache Airflow Providers

apache-airflow-providers-amazon==7.1.0

### Apache Airflow version

2.5.1

### Operating System

Ubuntu 18.04

### Deployment

Official Apache Airflow Helm Chart

### Deployment details

_No response_

### What happened

When looking at logs in the UI for a running task when using remote s3 logging, the logs for the task are only uploaded to s3 after the task has completed. The the `S3TaskHandler` falls back to the local logs stored on the worker in that case (by falling back to the `FileTaskHandler` behavior) and prepends the line `*** Falling back to local log` to those logs.

This is mostly fine, but for the new log streaming behavior, this means that `*** Falling back to local log` is returned from `/get_logs_with_metadata` on each call, even if there are no new logs.

### What you think should happen instead

I'd expect the falling back message only to be included in calls with no `log_pos` in the metadata or with a `log_pos` of `0`.

### How to reproduce

Start a task with `logging.remote_logging` set to `True` and `logging.remote_base_log_folder` set to `s3://something` and watch the logs while the task is running. You'll see `*** Falling back to local log` printed every few seconds.

### Anything else

_No response_

### Are you willing to submit PR?

- [X] Yes I am willing to submit a PR!

### Code of Conduct

- [X] I agree to follow this project's [Code of Conduct](https://github.com/apache/airflow/blob/main/CODE_OF_CONDUCT.md)

"""Close and upload local log file to remote storage S3."""
        
        
        
        
        if self.closed:
            return
        super().close()
        if not self.upload_on_close:
            return
        local_loc = os.path.join(self.local_base, self.log_relative_path)
        remote_loc = os.path.join(self.remote_base, self.log_relative_path)
        if os.path.exists(local_loc):
            
            log = pathlib.Path(local_loc).read_text()
            self.s3_write(log, remote_loc)
        
        self.closed = True
    def _read_remote_logs(self, ti, try_number, metadata=None):