### 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
self,
        dag_runs: Iterable[DagRun],
        dag: DAG,
        base_date: DateTime,
        session: settings.Session,
    ):
        """Returns formatted dag_runs for Tree view"""
        dates = sorted(dag_runs.keys())
        min_date = min(dag_runs, default=None)
        task_instances = {
            (ti.task_id, ti.execution_date): ti
            for ti in dag.get_task_instances(start_date=min_date, end_date=base_date, session=session)
        }
        expanded = set()
        
        
        
        node_count = 0
        node_limit = 5000 / max(1, len(dag.leaves))
        def encode_ti(task_instance: Optional[models.TaskInstance]) -> Optional[List]: