### 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)

"""
        A restful endpoint that returns external links for a given Operator.
        It queries the operator that sent the request for the links it wishes
        to provide for a given external link name.
        API: GET
        Args: dag_id: The id of the dag containing the task in question
              task_id: The id of the task in question
              execution_date: The date of execution of the task
              link_name: The name of the link reference to find the actual URL for
        Returns:
            200: {url: <url of link>, error: None} - returned when there was no problem
                finding the URL
            404: {url: None, error: <error message>} - returned when the operator does
                not return a URL
        """
        dag_id = request.args.get("dag_id")
        task_id = request.args.get("task_id")
        map_index = request.args.get("map_index", -1, type=int)
        execution_date = request.args.get("execution_date")
        dttm = _safe_parse_datetime(execution_date)
        dag = get_airflow_app().dag_bag.get_dag(dag_id)
        if not dag or task_id not in dag.task_ids:
            return {"url": None, "error": f"can't find dag {dag} or task_id {task_id}"}, 404
        task: AbstractOperator = dag.get_task(task_id)
        link_name = request.args.get("link_name")