### 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
"""Shows task instances."""
        dag_id = request.args.get('dag_id')
        dag = current_app.dag_bag.get_dag(dag_id)
        dttm = request.args.get('execution_date')
        if dttm:
            dttm = timezone.parse(dttm)
        else:
            return "Error: Invalid execution_date"
        task_instances = {ti.task_id: alchemy_to_dict(ti) for ti in dag.get_task_instances(dttm, dttm)}
        return json.dumps(task_instances, cls=utils_json.AirflowJsonEncoder)
    @expose('/object/tree_data')
    @auth.has_access(
        [
            (permissions.ACTION_CAN_READ, permissions.RESOURCE_DAG),
            (permissions.ACTION_CAN_READ, permissions.RESOURCE_TASK_INSTANCE),
        ]
    )
    @action_logging
    def tree_data(self):
        """Returns tree data"""
        dag_id = request.args.get('dag_id')
        dag = current_app.dag_bag.get_dag(dag_id)
        if not dag:
            response = jsonify({'error': f"can't find dag {dag_id}"})
            response.status_code = 404
            return response
        root = request.args.get('root')
        if root: