### Apache Airflow version

2.2.0

### Operating System

Debian buster

### Versions of Apache Airflow Providers

_No response_

### Deployment

Astronomer

### Deployment details

astro dev start

### What happened

When I have tried to duplicate a connection first time it has created a connection with hello_copy1 and duplicating the same connection second time giving me an error of 
```Connection hello_copy2 can't be added. Integrity error, probably unique constraint.```




### What you expected to happen

It should create a connection with name hello_copy3 or the error message should be more user friendly.

### How to reproduce

https://github.com/apache/airflow/pull/15574#issuecomment-912438705

### Anything else

Suggested Error 
```
Connection hello_copy2 can't be added because it already exists.
```
or
Change the number logic in _copyN so the new name will be always unique.


### Are you willing to submit PR?

- [ ] 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)

airflow/www/views.py
"""
        An endpoint helping check the health status of the Airflow instance,
        including metadatabase and scheduler.
        """
        payload = {'metadatabase': {'status': 'unhealthy'}}
        latest_scheduler_heartbeat = None
        scheduler_status = 'unhealthy'
        payload['metadatabase'] = {'status': 'healthy'}
        try:
            scheduler_job = SchedulerJob.most_recent_job()
            if scheduler_job:
                latest_scheduler_heartbeat = scheduler_job.latest_heartbeat.isoformat()
                if scheduler_job.is_alive():
                    scheduler_status = 'healthy'
        except Exception:
            payload['metadatabase']['status'] = 'unhealthy'
        payload['scheduler'] = {
            'status': scheduler_status,
            'latest_scheduler_heartbeat': latest_scheduler_heartbeat,
        }
        return wwwutils.json_response(payload)
    @expose('/home')
    @auth.has_access(
        [
            (permissions.ACTION_CAN_READ, permissions.RESOURCE_WEBSITE),
        ]
    )
    def index(self):