### Apache Airflow version

2.7.0

### What happened

On the DAGs page, the All, Active, and Paused counts include deleted DAGs. This is different from <= 2.6.1 (at least), where they were not included in the totals. Specifically this is for DAGs for which the DAG files have been removed, not DAGs that have been deleted via the UI.

### What you think should happen instead

Including deleted DAGs in those counts is confusing, and this behavior should revert to the previous behavior.

### How to reproduce

Create a DAG. 
Wait for totals to increment.
Remove the DAG file.

The totals will not change.

### Operating System

Debian GNU/Linux 11 (bullseye)

### Versions of Apache Airflow Providers

```apache-airflow-providers-amazon==8.5.1
apache-airflow-providers-celery==3.3.2
apache-airflow-providers-cncf-kubernetes==7.4.2
apache-airflow-providers-common-sql==1.7.0
apache-airflow-providers-datadog==3.3.1
apache-airflow-providers-elasticsearch==5.0.0
apache-airflow-providers-ftp==3.5.0
apache-airflow-providers-google==10.6.0
apache-airflow-providers-http==4.5.0
apache-airflow-providers-imap==3.3.0
apache-airflow-providers-microsoft-azure==6.2.4
apache-airflow-providers-postgres==5.6.0
apache-airflow-providers-redis==3.3.1
apache-airflow-providers-salesforce==5.4.1
apache-airflow-providers-slack==7.3.2
apache-airflow-providers-snowflake==4.4.2
apache-airflow-providers-sqlite==3.4.3
```

### Deployment

Astronomer

### Deployment details

_No response_

### Anything else

I suspect the issue is with [DagModel.deactivate_deleted_dags](https://github.com/apache/airflow/blob/f971ba2f2f9703d0e1954e52aaded52a83c2f844/airflow/models/dag.py#L3564), but I'm unable to verify.



### 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)

"""
    Remove all parameters starting with `_`.
    :param args: arguments of request
    :return: copy of the dictionary passed as input with args starting with `_` removed.
    """
    return {key: value for key, value in args.items() if not key.startswith("_")}
#
#
#
_WHATWG_C0_CONTROL_OR_SPACE = (
    "\x00\x01\x02\x03\x04\x05\x06\x07\x08\t\n\x0b\x0c"
    "\r\x0e\x0f\x10\x11\x12\x13\x14\x15\x16\x17\x18\x19\x1a\x1b\x1c\x1d\x1e\x1f "
)
def get_safe_url(url):
    """Given a user-supplied URL, ensure it points to our web server."""
    if not url:
        return url_for("Airflow.index")
    
    
    if ";" in unquote(url):
        return url_for("Airflow.index")
    url = url.lstrip(_WHATWG_C0_CONTROL_OR_SPACE)
    host_url = urlsplit(request.host_url)
    redirect_url = urlsplit(urljoin(request.host_url, url))
    if not (redirect_url.scheme in ("http", "https") and host_url.netloc == redirect_url.netloc):
        return url_for("Airflow.index")
    
    return redirect_url.geturl()
def get_date_time_num_runs_dag_runs_form_data(www_request, session, dag):