### 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
node[children_key] = children
            if task.depends_on_past:
                node['depends_on_past'] = task.depends_on_past
            if task.start_date:
                
                node['start_ts'] = int(task.start_date.timestamp())
                if task.end_date:
                    
                    node['end_ts'] = int(task.end_date.timestamp())
            if task.extra_links:
                node['extra_links'] = task.extra_links
            return node
        return {
            'name': '[DAG]',
            'children': [recurse_nodes(t, set()) for t in dag.roots],
            'instances': [dag_runs.get(d) or {'execution_date': d.isoformat()} for d in dates],
        }
    @expose('/tree')
    @auth.has_access(
        [
            (permissions.ACTION_CAN_READ, permissions.RESOURCE_DAG),
            (permissions.ACTION_CAN_READ, permissions.RESOURCE_TASK_INSTANCE),
            (permissions.ACTION_CAN_READ, permissions.RESOURCE_TASK_LOG),
        ]
    )
    @gzipped
    @action_logging
    @provide_session
    def tree(self, session=None):
        """Get Dag as tree."""