Checklist

• I have verified that the issue exists against the main branch of Celery.
• This has already been asked to the discussions forum first.
• I have read the relevant section in the
  contribution guide
  on reporting bugs.
• I have checked the issues list
  for similar or identical bug reports.
• I have checked the pull requests list
  for existing proposed fixes.
• I have checked the commit log
  to find out if the bug was already fixed in the main branch.
• I have included all related issues and possible duplicate issues
  in this issue (If there are none, check this box anyway).
• I have tried to reproduce the issue with pytest-celery and added the reproduction script below.

Mandatory Debugging Information

• I have included the output of celery -A proj report in the issue.
• I have verified that the issue exists against the main branch of Celery.
• I have included the contents of pip freeze in the issue.
• I have included all the versions of all the external dependencies required
  to reproduce this bug.

Optional Debugging Information

• I have tried reproducing the issue on more than one Python version
  and/or implementation.
• I have tried reproducing the issue on more than one message broker and/or
  result backend.
• I have tried reproducing the issue on more than one version of the message
  broker and/or result backend.
• I have tried reproducing the issue on more than one operating system.
• I have tried reproducing the issue on more than one workers pool.
• I have tried reproducing the issue with autoscaling, retries,
  ETA/Countdown & rate limits disabled.
• I have tried reproducing the issue after downgrading
  and/or upgrading Celery and its dependencies.

Related Issues and Possible Duplicates

N/A

Environment & Settings

software -> celery:5.5.0rc4 (immunity) kombu:5.5.0rc2 py:3.9.20
            billiard:4.2.1 py-amqp:5.3.1   
platform -> system:Linux arch:64bit
            kernel version:6.10.14-linuxkit imp:CPython
loader   -> celery.loaders.app.AppLoader
settings -> transport:amqp results:django-db

Steps to Reproduce

Required Dependencies

• Minimal Python Version: 3.9.20
• Minimal Celery Version: 5.5.0rc4
• Minimal Kombu Version: 5.5.0rc2
• Minimal Broker Version: RabbitMQ 3.13.7
• Minimal Result Backend Version: PG 17.0
• Minimal OS and/or Kernel Version: Debian Bookworm
• Minimal Broker Client Version: py-amqp 5.3.1
• Minimal Result Backend Client Version: django-celery-results 2.5.`

Python Packages

celery==5.5.0rc4
django==3.2.25
django-celery-results==2.5.1

Other Dependencies

N/A

Minimally Reproducible Test Case

1. Start celery with REMAP_SIGTERM=SIGQUIT
2. Start a long running task
3. Stop celery with kill -s TERM
4. Observe the task completing but celery not exiting
5. Verify that status is FAILURE even though it should be SUCCESS

Example in this repo:
https://github.com/daveisfera/celery_cold_shutdown

Logs:

[2025-01-21 02:29:20,211: WARNING/ForkPoolWorker-1] Value: 8

worker: Hitting Ctrl+C again will terminate all running tasks!
[2025-01-21 02:29:21,132: WARNING/MainProcess] Initiating Soft Shutdown, terminating in 16 seconds
[2025-01-21 02:29:28,220: WARNING/ForkPoolWorker-1] Done: 8
[2025-01-21 02:29:28,228: INFO/ForkPoolWorker-1] Task mysite.celery.long_task[97636c13-9c46-4880-8f31-76b277a37bf5] succeeded in 8.017255892998946s: None
[2025-01-21 02:29:37,167: ERROR/MainProcess] Task handler raised error: TimeLimitExceeded(15)
Traceback (most recent call last):
  File "/usr/local/lib/python3.9/site-packages/billiard/pool.py", line 684, in on_hard_timeout
    raise TimeLimitExceeded(job._timeout)
billiard.einfo.ExceptionWithTraceback: 
"""
Traceback (most recent call last):
  File "/usr/local/lib/python3.9/site-packages/billiard/pool.py", line 684, in on_hard_timeout
    raise TimeLimitExceeded(job._timeout)
billiard.exceptions.TimeLimitExceeded: TimeLimitExceeded(15,)
"""
[2025-01-21 02:29:37,167: ERROR/MainProcess] Hard time limit (15s) exceeded for mysite.celery.long_task[97636c13-9c46-4880-8f31-76b277a37bf5]

worker: Cold shutdown (MainProcess)

NOTE: I'm not familiar enough with the testing setup to add this as a test, but it's pretty straightforward to reproduce and the example repo I linked to can show it

Expected Behavior

Tasks that complete when a cold shutdown is happening should be reported as SUCCESS

Actual Behavior

Tasks that complete when a cold shutdown is happening are timing out and reported as FAILURE