DagProcessor pod crashes regulary on Openshift due to stale filehandler

### Under which category would you file this issue?

Airflow Core

### Apache Airflow version

3.2.2

### What happened and how to reproduce it?

In Openshift we see a lot of restarts related to the DagProcessor pod.

When checking the previous logs of the crashed pod, we can clearly see the reason why the pod was restarted.

```
2026-07-03T08:59:25.767332Z [info ] Process exited [supervisor] exit_code= loc=supervisor.py:859 pid=11928 signal_sent=SIGTERM
2026-07-03T08:59:25.843704Z [info ] Waiting up to 5 seconds for processes to exit... [airflow.utils.process_utils] loc=process_utils.py:308
Traceback (most recent call last):
File "/usr/local/sbin/airflow", line 10, in
sys.exit(main())
~~~~^^
File "/usr/local/lib/python3.13/site-packages/airflow/__main__.py", line 55, in main
args.func(args)
~~~~~~~~~^^^^^^
File "/usr/local/lib/python3.13/site-packages/airflow/cli/cli_config.py", line 49, in command
return func(*args, **kwargs)
File "/usr/local/lib/python3.13/site-packages/airflow/utils/memray_utils.py", line 60, in wrapper
return func(*args, **kwargs)
File "/usr/local/lib/python3.13/site-packages/airflow/utils/cli.py", line 113, in wrapper
return f(*args, **kwargs)
File "/usr/local/lib/python3.13/site-packages/airflow/utils/providers_configuration_loader.py", line 54, in wrapped_function
return func(*args, **kwargs)
File "/usr/local/lib/python3.13/site-packages/airflow/cli/commands/dag_processor_command.py", line 64, in dag_processor
run_command_with_daemon_option(
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~^
args=args,
^^^^^^^^^^
...<2 lines>...
should_setup_logging=True,
^^^^^^^^^^^^^^^^^^^^^^^^^^
)
^
File "/usr/local/lib/python3.13/site-packages/airflow/cli/commands/daemon_utils.py", line 86, in run_command_with_daemon_option
callback()
~~~~~~~~^^
File "/usr/local/lib/python3.13/site-packages/airflow/cli/commands/dag_processor_command.py", line 67, in
callback=lambda: run_job(job=job_runner.job, execute_callable=job_runner._execute),
~~~~~~~^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
File "/usr/local/lib/python3.13/site-packages/airflow/utils/session.py", line 100, in wrapper
return func(*args, session=session, **kwargs) # type: ignore[arg-type]
File "/usr/local/lib/python3.13/site-packages/airflow/jobs/job.py", line 355, in run_job
return execute_job(job, execute_callable=execute_callable)
File "/usr/local/lib/python3.13/site-packages/airflow/jobs/job.py", line 384, in execute_job
ret = execute_callable()
File "/usr/local/lib/python3.13/site-packages/airflow/jobs/dag_processor_job_runner.py", line 61, in _execute
self.processor.run()
~~~~~~~~~~~~~~~~~~^^
File "/usr/local/lib/python3.13/site-packages/airflow/dag_processing/manager.py", line 334, in run
return self._run_parsing_loop()
~~~~~~~~~~~~~~~~~~~~~~^^
File "/usr/local/lib/python3.13/site-packages/airflow/dag_processing/manager.py", line 453, in _run_parsing_loop
self._collect_results()
~~~~~~~~~~~~~~~~~~~~~^^
File "/usr/local/lib/python3.13/site-packages/airflow/utils/session.py", line 100, in wrapper
return func(*args, session=session, **kwargs) # type: ignore[arg-type]
File "/usr/local/lib/python3.13/site-packages/airflow/dag_processing/manager.py", line 979, in _collect_results
processor.logger_filehandle.close()
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~^^
OSError: [Errno 116] Stale file handle
```

### What you think should happen instead?

The OSError should be catched when file handler is stale and logged as a warning but not propageted as this would avoid the pod from crashing and thus being restarted each time.

### Operating System

Red Hat Fedora 5.3

### Deployment

Official Apache Airflow Helm Chart

### Apache Airflow Provider(s)

_No response_

### Versions of Apache Airflow Providers

_No response_

### Official Helm Chart version

1.22.0 (latest released)

### Kubernetes Version

v1.29.14+41c4e9b

### Helm Chart configuration

_No response_

### Docker Image customizations

_No response_

### Anything else?

Multiple times a day

### 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)