### Apache Airflow version

2.6.0

### What happened

Stream logging works as long as the task is running. Once the task finishes, no logs are printed to the UI (only the hostname of the worker is printed)
<img width="1657" alt="image" src="https://user-images.githubusercontent.com/16529101/236212701-aecf6cdc-4d87-4817-a685-0778b94d182b.png">


### What you think should happen instead

Expected to see the complete log of a task

### How to reproduce

Start an airflow task. You should be able to see the logs coming in as a stream, once it finishes, the logs are gone

### Operating System

CentOS 7

### Versions of Apache Airflow Providers

airflow-provider-great-expectations==0.1.5
apache-airflow==2.6.0
apache-airflow-providers-airbyte==3.1.0
apache-airflow-providers-apache-hive==4.0.1
apache-airflow-providers-apache-spark==3.0.0
apache-airflow-providers-celery==3.1.0
apache-airflow-providers-common-sql==1.4.0
apache-airflow-providers-ftp==3.3.1
apache-airflow-providers-http==4.3.0
apache-airflow-providers-imap==3.1.1
apache-airflow-providers-mysql==5.0.0
apache-airflow-providers-oracle==3.4.0
apache-airflow-providers-postgres==5.4.0
apache-airflow-providers-sqlite==3.3.2

### Deployment

Virtualenv installation

### Deployment details

Celery with 4 workers nodes/VMs. Scheduler and Webserver on a different VM

### Anything else

_No response_

### Are you willing to submit PR?

- [ ] 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)

ti.log.disabled = False
        file_handler = next(
            (handler for handler in logger.handlers if handler.name == FILE_TASK_HANDLER), None
        )
        assert file_handler is not None
        set_context(logger, ti)
        assert file_handler.handler is not None
        
        log_filename = file_handler.handler.baseFilename
        assert os.path.isfile(log_filename)
        assert log_filename.endswith("1.log"), log_filename
        ti.run(ignore_ti_state=True)
        file_handler.flush()
        file_handler.close()
        assert hasattr(file_handler, "read")
        
        logs, metadatas = file_handler.read(ti)
        assert isinstance(logs, list)
        assert isinstance(metadatas, list)
        assert len(logs) == 1
        assert len(logs) == len(metadatas)
        assert isinstance(metadatas[0], dict)
        target_re = r"\n\[[^\]]+\] {test_log_handlers.py:\d+} INFO - test\n"
        
        
        assert re.search(target_re, logs[0][0][-1]), "Logs were " + str(logs)
        
        os.remove(log_filename)
    def test_file_task_handler_running(self):
        def task_callable(ti):