### 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)

#
#
#
from __future__ import annotations
import os
import pathlib
from airflow.compat.functools import cached_property
from airflow.configuration import conf
from airflow.providers.amazon.aws.hooks.s3 import S3Hook
from airflow.utils.log.file_task_handler import FileTaskHandler
from airflow.utils.log.logging_mixin import LoggingMixin
class S3TaskHandler(FileTaskHandler, LoggingMixin):
    """
    S3TaskHandler is a python log handler that handles and reads
    task instance logs. It extends airflow FileTaskHandler and
    uploads to and reads from S3 remote storage.
    """
    trigger_should_wrap = True
    def __init__(self, base_log_folder: str, s3_log_folder: str, filename_template: str | None = None):