### Body

We have several tests marked in the code base with `@pytest.mark.quarantined`
It means that the tests are flaky and if fail in CI it does not fail the build.
The goal is to fix the tests and make them stable.

This task is to gather all of them under the same issue instead of dedicated issue per test.

- [x] [TestImpersonation](https://github.com/apache/airflow/blob/bfcae349b88fd959e32bfacd027a5be976fe2132/tests/core/test_impersonation_tests.py#L117)
- [x] [TestImpersonationWithCustomPythonPath](https://github.com/apache/airflow/blob/bfcae349b88fd959e32bfacd027a5be976fe2132/tests/core/test_impersonation_tests.py#L181)
- [x] [test_exception_propagation](https://github.com/apache/airflow/blob/76f81cd4a7433b7eeddb863b2ae6ee59176cf816/tests/jobs/test_local_task_job.py#L772)
- [x] [test_localtaskjob_maintain_heart_rate](https://github.com/apache/airflow/blob/76f81cd4a7433b7eeddb863b2ae6ee59176cf816/tests/jobs/test_local_task_job.py#L402)
- [x] [test_exception_propagation](https://github.com/apache/airflow/blob/4d0fd8ef6adc35f683c7561f05688a65fd7451f4/tests/executors/test_celery_executor.py#L103)
- [x] [test_process_sigterm_works_with_retries](https://github.com/apache/airflow/blob/65010fda091242870a410c65478eae362899763b/tests/jobs/test_local_task_job.py#L770)


### Committer

- [X] I acknowledge that I am a maintainer/committer of the Apache Airflow project.
ti.state = State.RUNNING
        ti.pid = 2
        
        
        assert job1.task_runner.run_as_user == "testuser"
        session.merge(ti)
        session.commit()
        job1.heartbeat_callback(session=None)
        
        
        job1.task_runner.process.pid = 2
        with pytest.raises(AirflowException, match="PID of job runner does not match"):
            job1.heartbeat_callback()
        
        
        ti.pid = None
        session.merge(ti)
        session.commit()
        assert job1.task_runner.run_as_user == "testuser"
        assert ti.run_as_user is None
        assert ti.pid != job1.task_runner.process.pid
        job1.heartbeat_callback()
    def test_heartbeat_failed_fast(self):
        """
        Test that task heartbeat will sleep when it fails fast
        """
        self.mock_base_job_sleep.side_effect = time.sleep
        dag_id = "test_heartbeat_failed_fast"
        task_id = "test_heartbeat_failed_fast_op"
        with create_session() as session: