Someties test_cli_webserver_background sometimes detect processes left behind

### Body

Sometimes (rather rarely) the "check_processes" in
`tests/cli/commands/test_webserver_command.py::TestCliWebServer::test_cli_webserver_background` detects some remaining processes.

This is likely a side effect of other test.

Example failure:

https://github.com/ache/airflow/actions/runs/6996129264/job/19031743272?pr=35862

```
________________ TestCliWebServer.test_cli_webserver_background ________________

self =
tmp_path = PosixPath('/tmp/pytest-of-root/pytest-0/test_cli_webserver_background0')

@pytest.mark.execution_timeout(210)
def test_cli_webserver_background(self, tmp_path):
with mock.patch.dict(
"os.environ",
AIRFLOW__CORE__DAGS_FOLDER="/dev/null",
AIRFLOW__CORE__LOAD_EXAMPLES="False",
AIRFLOW__WEBSERVER__WORKERS="1",
):
pidfile_webserver = tmp_path / "pidflow-webserver.pid"
pidfile_monitor = tmp_path / "pidflow-webserver-monitor.pid"
stdout = tmp_path / "airflow-webserver.out"
stderr = tmp_path / "airflow-webserver.err"
logfile = tmp_path / "airflow-webserver.log"
try:
# Run webserver as daemon in background. Note that the wait method is not called.

proc = subprocess.Popen(
[
"airflow",
"webserver",
"--daemon",
"--pid",
os.fspath(pidfile_webserver),
"--stdout",
os.fspath(stdout),
"--stderr",
os.fspath(stderr),
"--log-file",
os.fspath(logfile),
]
)
assert proc.poll() is None

pid_monitor = self._wait_pidfile(pidfile_monitor)
console.print(f"[blue]Monitor started at {pid_monitor}")
pid_webserver = self._wait_pidfile(pidfile_webserver)
console.print(f"[blue]Webserver started at {pid_webserver}")
console.print("[blue]Running airflow webserver process:")
# Assert that the webserver and gunicorn processes are running (by name rather than pid).
assert self._find_process(r"airflow webserver", print_found_process=True)
console.print("[blue]Waiting for gunicorn processes:")
# wait for gunicorn to start
for i in range(30):
if self._find_process(r"^gunicorn"):
> raise AssertionError(
"Background processes are running that prevent the test from passing successfully."
)
E AssertionError: Background processes are running that prevent the test from passing successfully.

tests/cli/commands/_common_cli_classes.py:72: AssertionError
----------------------------- Captured stdout call -----------------------------
Waiting for pidfile /tmp/pytest-of-root/pytest-0/test_cli_webserver_background0/pidflow-webserver-monitor.pid to be created ...
Waiting for pidfile /tmp/pytest-of-root/pytest-0/test_cli_webserver_background0/pidflow-webserver-monitor.pid to be created ...
Waiting for pidfile /tmp/pytest-of-root/pytest-0/test_cli_webserver_background0/pidflow-webserver-monitor.pid to be created ...
Waiting for pidfile /tmp/pytest-of-root/pytest-0/test_cli_webserver_background0/pidflow-webserver-monitor.pid to be created ...
Waiting for pidfile /tmp/pytest-of-root/pytest-0/test_cli_webserver_background0/pidflow-webserver-monitor.pid to be created ...
Waiting for pidfile /tmp/pytest-of-root/pytest-0/test_cli_webserver_background0/pidflow-webserver-monitor.pid to be created ...
Waiting for pidfile /tmp/pytest-of-root/pytest-0/test_cli_webserver_background0/pidflow-webserver-monitor.pid to be created ...
____________ _____________
____ |__( )_________ __/__ /________ __
____ /| |_ /__ ___/_ /_ __ /_ __ \_ | /| / /
___ ___ | / _ / _ __/ _ / / /_/ /_ |/ |/ /
_/_/ |_/_/ /_/ /_/ /_/ \____/____/|__/
Running the Gunicorn Server with:
Workers: 1 sync
Host: 0.0.0.0:8080
Timeout: 120
Logfiles: - -
Access Logformat:
=================================================================
[2023-11-26T14:43:32.521+0000] {dagbag.py:538} INFO - Filling up the DagBag from /dev/null
Please make sure to build the frontend in static/ directory and restart the server
[2023-11-26T14:43:32.822+0000] {override.py:872} WARNING - No user yet created, use flask fab command to do it.
Waiting for pidfile /tmp/pytest-of-root/pytest-0/test_cli_webserver_background0/pidflow-webserver-monitor.pid to be created ...
Waiting for pidfile /tmp/pytest-of-root/pytest-0/test_cli_webserver_background0/pidflow-webserver-monitor.pid to be created ...
Waiting for pidfile /tmp/pytest-of-root/pytest-0/test_cli_webserver_background0/pidflow-webserver-monitor.pid to be created ...
[2023-11-26T14:43:36.046+0000] {options.py:83} WARNING - The swagger_ui directory could not be found.
Please install connexion with extra install: pip install connexion[swagger-ui]
or provide the path to your local installation by passing swagger_path=

[2023-11-26T14:43:36.046+0000] {options.py:83} WARNING - The swagger_ui directory could not be found.
Please install connexion with extra install: pip install connexion[swagger-ui]
or provide the path to your local installation by passing swagger_path=

Waiting for pidfile /tmp/pytest-of-root/pytest-0/test_cli_webserver_background0/pidflow-webserver-monitor.pid to be created ...
Monitor started at 254
Waiting for pidfile /tmp/pytest-of-root/pytest-0/test_cli_webserver_background0/pidflow-webserver.pid to be created ...
Waiting for pidfile /tmp/pytest-of-root/pytest-0/test_cli_webserver_background0/pidflow-webserver.pid to be created ...
Waiting for pidfile /tmp/pytest-of-root/pytest-0/test_cli_webserver_background0/pidflow-webserver.pid to be created ...
Waiting for pidfile /tmp/pytest-of-root/pytest-0/test_cli_webserver_background0/pidflow-webserver.pid to be created ...
Waiting for pidfile /tmp/pytest-of-root/pytest-0/test_cli_webserver_background0/pidflow-webserver.pid to be created ...
Waiting for pidfile /tmp/pytest-of-root/pytest-0/test_cli_webserver_background0/pidflow-webserver.pid to be created ...
Waiting for pidfile /tmp/pytest-of-root/pytest-0/test_cli_webserver_background0/pidflow-webserver.pid to be created ...
Waiting for pidfile /tmp/pytest-of-root/pytest-0/test_cli_webserver_background0/pidflow-webserver.pid to be created ...
Webserver started at 258
Running airflow webserver process:
{
'cmdline': [
'/usr/local/bin/python',
'/usr/local/bin/airflow',
'webserver',
'--daemon',
'--pid',
'/tmp/pytest-of-root/pytest-0/test_cli_webserver_background0/pidflow-webserver.pid',
'--stdout',
'/tmp/pytest-of-root/pytest-0/test_cli_webserver_background0/airflow-webserver.out',
'--stderr',
'/tmp/pytest-of-root/pytest-0/test_cli_webserver_background0/airflow-webserver.err',
'--log-file',
'/tmp/pytest-of-root/pytest-0/test_cli_webserver_background0/airflow-webserver.log'
],
'pid': 254,
'name': 'airflow'
}
Waiting for gunicorn processes:
Waiting for gunicorn to start ...
Waiting for gunicorn to start ...
Waiting for gunicorn to start ...
Waiting for gunicorn to start ...
Waiting for gunicorn to start ...
Waiting for gunicorn to start ...
Waiting for gunicorn to start ...
Waiting for gunicorn to start ...
Running gunicorn processes:
{
'cmdline': [
'gunicorn: master [airflow-webserver]',
'',
'',
'',
'',
'',
........... LONG LIST HERE ........
''
],
'pid': 258,
'name': 'gunicorn: master [airflow-webserver]'
}
Here list of processes ends
Forcefully killing all gunicorn processes
Exception occurred. Dumping all logs.
Dumping /tmp/pytest-of-root/pytest-0/test_cli_webserver_background0/airflow-webserver.err (size: 2775)
Traceback (most recent call last):
File "/usr/local/lib/python3.8/site-packages/psutil/_psposix.py", line 121, in wait_pid
retpid, status = os.waitpid(pid, flags)
ChildProcessError: [Errno 10] No child processes

During handling of the above exception, another exception occurred:

Traceback (most recent call last):
File "/usr/local/bin/airflow", line 33, in
sys.exit(load_entry_point('apache-airflow', 'console_scripts', 'airflow')())
File "/opt/airflow/airflow/__main__.py", line 57, in main
args.func(args)
File "/opt/airflow/airflow/cli/cli_config.py", line 49, in command
return func(*args, **kwargs)
File "/opt/airflow/airflow/utils/cli.py", line 114, in wrapper
return f(*args, **kwargs)
File "/opt/airflow/airflow/utils/providers_configuration_loader.py", line 55, in wrapped_function
return func(*args, **kwargs)
File "/opt/airflow/airflow/cli/commands/webserver_command.py", line 484, in webserver
run_command_with_daemon_option(
File "/opt/airflow/airflow/cli/commands/daemon_utils.py", line 81, in run_command_with_daemon_option
callback()
File "/opt/airflow/airflow/cli/commands/webserver_command.py", line 487, in
callback=lambda: start_and_monitor_gunicorn(args),
File "/opt/airflow/airflow/cli/commands/webserver_command.py", line 471, in start_and_monitor_gunicorn
monitor_gunicorn(gunicorn_master_proc)
File "/opt/airflow/airflow/cli/commands/webserver_command.py", line 447, in monitor_gunicorn
GunicornMonitor(
File "/opt/airflow/airflow/cli/commands/webserver_command.py", line 217, in start
self._check_workers()
File "/opt/airflow/airflow/cli/commands/webserver_command.py", line 241, in _check_workers
sleep(1)
File "/opt/airflow/airflow/cli/commands/webserver_command.py", line 444, in
signal.signal(signal.SIGTERM, lambda signum, _: kill_proc(signum, gunicorn_master_proc))
File "/opt/airflow/airflow/cli/commands/webserver_command.py", line 432, in kill_proc
gunicorn_master_proc.wait(timeout=30)
File "/usr/local/lib/python3.8/site-packages/psutil/__init__.py", line 1294, in wait
self._exitcode = self._proc.wait(timeout)
File "/usr/local/lib/python3.8/site-packages/psutil/_pslinux.py", line 1650, in wrapper
return fun(self, *args, **kwargs)
File "/usr/local/lib/python3.8/site-packages/psutil/_pslinux.py", line 1873, in wait
return _psposix.wait_pid(self.pid, timeout, self._name)
File "/usr/local/lib/python3.8/site-packages/psutil/_psposix.py", line 132, in wait_pid
interval = sleep(interval)
File "/usr/local/lib/python3.8/site-packages/psutil/_psposix.py", line 114, in sleep
raise TimeoutExpired(timeout, pid=pid, name=proc_name)
psutil.TimeoutExpired: timeout after 30 seconds (pid=258)

```

### Committer

- [X] I acknowledge that I am a maintainer/committer of the Apache Airflow project.

Start with tests/cli/commands/test_webserver_command.py::TestCliWebServer::test_cli_webserver_background and the check_processes logic in tests/cli/commands/_common_cli_classes.py. Trace the daemon monitoring and cleanup paths in airflow/cli/commands/webserver_command.py, using the linked failure as a reproduction reference. Done means the test no longer detects leftover gunicorn or webserver processes and remains reliable.

Written by the indexing model from the issue text.