### 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
dags_query = session.query(DagModel).filter(~DagModel.is_subdag, DagModel.is_active)
            if arg_search_query:
                dags_query = dags_query.filter(
                    DagModel.dag_id.ilike('%' + arg_search_query + '%')
                    | DagModel.owners.ilike('%' + arg_search_query + '%')
                )
            if arg_tags_filter:
                dags_query = dags_query.filter(DagModel.tags.any(DagTag.name.in_(arg_tags_filter)))
            dags_query = dags_query.filter(DagModel.dag_id.in_(filter_dag_ids))
            all_dags = dags_query
            active_dags = dags_query.filter(~DagModel.is_paused)
            paused_dags = dags_query.filter(DagModel.is_paused)
            is_paused_count = dict(
                all_dags.with_entities(DagModel.is_paused, func.count(DagModel.dag_id))
                .group_by(DagModel.is_paused)
                .all()
            )
            status_count_active = is_paused_count.get(False, 0)
            status_count_paused = is_paused_count.get(True, 0)
            all_dags_count = status_count_active + status_count_paused
            if arg_status_filter == 'active':
                current_dags = active_dags
                num_of_all_dags = status_count_active
            elif arg_status_filter == 'paused':
                current_dags = paused_dags
                num_of_all_dags = status_count_paused
            else:
                current_dags = all_dags
                num_of_all_dags = all_dags_count
            dags = (