### 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
def trigger(self, session=None):
        """Triggers DAG Run."""
        dag_id = request.values.get('dag_id')
        origin = get_safe_url(request.values.get('origin'))
        unpause = request.values.get('unpause')
        request_conf = request.values.get('conf')
        request_execution_date = request.values.get('execution_date', default=timezone.utcnow().isoformat())
        is_dag_run_conf_overrides_params = conf.getboolean('core', 'dag_run_conf_overrides_params')
        dag = current_app.dag_bag.get_dag(dag_id)
        dag_orm = session.query(models.DagModel).filter(models.DagModel.dag_id == dag_id).first()
        if not dag_orm:
            flash(f"Cannot find dag {dag_id}")
            return redirect(origin)
        if request.method == 'GET':
            
            default_conf = ''
            doc_md = wwwutils.wrapped_markdown(getattr(dag, 'doc_md', None))
            form = DateTimeForm(data={'execution_date': request_execution_date})
            if request_conf:
                default_conf = request_conf
            else:
                try:
                    default_conf = json.dumps(
                        {str(k): v.resolve(suppress_exception=True) for k, v in dag.params.items()}, indent=4
                    )
                except TypeError:
                    flash("Could not pre-populate conf field due to non-JSON-serializable data-types")
            return self.render_template(
                'airflow/trigger.html',
                dag_id=dag_id,