### 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
"""Home view."""
        hide_paused_dags_by_default = conf.getboolean('webserver', 'hide_paused_dags_by_default')
        default_dag_run = conf.getint('webserver', 'default_dag_run_display_number')
        num_runs = request.args.get('num_runs', default=default_dag_run, type=int)
        current_page = request.args.get('page', default=0, type=int)
        arg_search_query = request.args.get('search')