### 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)

"""Mark DagRun success."""
        dag_id = request.form.get("dag_id")
        dag_run_id = request.form.get("dag_run_id")
        confirmed = request.form.get("confirmed") == "true"
        return self._mark_dagrun_state_as_success(dag_id, dag_run_id, confirmed)
    @expose("/dagrun_queued", methods=["POST"])
    @auth.has_access(
        [
            (permissions.ACTION_CAN_EDIT, permissions.RESOURCE_DAG),
            (permissions.ACTION_CAN_EDIT, permissions.RESOURCE_DAG_RUN),
        ]
    )
    @action_logging
    def dagrun_queued(self):
        """Queue DagRun so tasks that haven't run yet can be started."""
        dag_id = request.form.get("dag_id")
        dag_run_id = request.form.get("dag_run_id")
        confirmed = request.form.get("confirmed") == "true"
        return self._mark_dagrun_state_as_queued(dag_id, dag_run_id, confirmed)
    @expose("/dagrun_details")
    def dagrun_details(self):
        """Redirect to the GRID DAGRun page. This is avoids breaking links."""
        dag_id = request.args.get("dag_id")
        run_id = request.args.get("run_id")
        return redirect(url_for("Airflow.grid", dag_id=dag_id, dag_run_id=run_id))
    def _mark_task_instance_state(