### 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
"""View to provide autocomplete results"""
    @auth.has_access([(permissions.ACTION_CAN_READ, permissions.RESOURCE_DAG)])
    @provide_session
    @expose('/dagmodel/autocomplete')
    def autocomplete(self, session=None):
        """Autocomplete."""
        query = unquote(request.args.get('query', ''))
        if not query:
            return wwwutils.json_response([])
        
        dag_ids_query = session.query(DagModel.dag_id.label('item')).filter(
            ~DagModel.is_subdag, DagModel.is_active, DagModel.dag_id.ilike('%' + query + '%')
        )
        owners_query = session.query(func.distinct(DagModel.owners).label('item')).filter(
            ~DagModel.is_subdag, DagModel.is_active, DagModel.owners.ilike('%' + query + '%')
        )
        
        status = flask_session.get(FILTER_STATUS_COOKIE)
        if status == 'active':
            dag_ids_query = dag_ids_query.filter(~DagModel.is_paused)
            owners_query = owners_query.filter(~DagModel.is_paused)
        elif status == 'paused':
            dag_ids_query = dag_ids_query.filter(DagModel.is_paused)
            owners_query = owners_query.filter(DagModel.is_paused)
        filter_dag_ids = current_app.appbuilder.sm.get_accessible_dag_ids(g.user)
        dag_ids_query = dag_ids_query.filter(DagModel.dag_id.in_(filter_dag_ids))
        owners_query = owners_query.filter(DagModel.dag_id.in_(filter_dag_ids))
        payload = [row[0] for row in dag_ids_query.union(owners_query).limit(10).all()]
        return wwwutils.json_response(payload)
class DagDependenciesView(AirflowBaseView):