### 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
return self.render_template(
                        'airflow/trigger.html',
                        dag_id=dag_id,
                        origin=origin,
                        conf=request_conf,
                        form=form,
                        is_dag_run_conf_overrides_params=is_dag_run_conf_overrides_params,
                    )
            except json.decoder.JSONDecodeError:
                flash("Invalid JSON configuration, not parseable", "error")
                form = DateTimeForm(data={'execution_date': execution_date})
                return self.render_template(
                    'airflow/trigger.html',
                    dag_id=dag_id,
                    origin=origin,
                    conf=request_conf,
                    form=form,
                    is_dag_run_conf_overrides_params=is_dag_run_conf_overrides_params,
                )
        if unpause and dag.is_paused:
            models.DagModel.get_dagmodel(dag_id).set_is_paused(is_paused=False)
        try:
            dag.create_dagrun(
                run_type=DagRunType.MANUAL,
                execution_date=execution_date,
                data_interval=dag.timetable.infer_manual_data_interval(run_after=execution_date),
                state=State.QUEUED,
                conf=run_conf,
                external_trigger=True,
                dag_hash=current_app.dag_bag.dags_hash.get(dag_id),