### Apache Airflow version

main (development)

### What happened

Steps to reproduce:
1. run 2 replicas of scheduler
2. initiate shut down of one of the schedulers
3. In Airflow UI observe message
<img width="1162" alt="image" src="https://user-images.githubusercontent.com/1017130/205650336-fb1d8e39-2213-4aec-8530-abd1417db426.png">

3rd step should be done immediately after 2nd (refreshing UI page few times). 2nd and 3rd steps might be repeated for couple of times in order to reproduce.


### What you think should happen instead

Warning message shouldn't be displayed.

The issue is that for this warning message recent (with latest heartbet) scheduler job is fetched
https://github.com/apache/airflow/blob/f02a7e9a8292909b369daae6d573f58deed04440/airflow/jobs/base_job.py#L133.

And this may point to job which is not running (state!="running") and that is why we see warning message.
The warning message in this case is misleading as another replica of scheduler is running in parallel.

### How to reproduce

_No response_

### Operating System

Linux

### Versions of Apache Airflow Providers

_No response_

### Deployment

Composer

### Deployment details

_No response_

### Anything else

_No response_

### 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)

def abort():
            raise RuntimeError("fail")
        job = MockJob(abort)
        with raises(RuntimeError):
            job.run()
        assert job.state == State.FAILED
        assert job.end_date is not None
    def test_most_recent_job(self):