### 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
origin=origin,
                conf=default_conf,
                doc_md=doc_md,
                form=form,
                is_dag_run_conf_overrides_params=is_dag_run_conf_overrides_params,
            )
        try:
            execution_date = timezone.parse(request_execution_date)
        except ParserError:
            flash("Invalid execution date", "error")
            form = DateTimeForm(data={'execution_date': timezone.utcnow().isoformat()})
            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,
            )
        dr = DagRun.find(dag_id=dag_id, execution_date=execution_date, run_type=DagRunType.MANUAL)
        if dr:
            flash(f"This run_id {dr.run_id} already exists")
            return redirect(origin)
        run_conf = {}
        if request_conf:
            try:
                run_conf = json.loads(request_conf)
                if not isinstance(run_conf, dict):
                    flash("Invalid JSON configuration, must be a dict", "error")
                    form = DateTimeForm(data={'execution_date': execution_date})