### 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)

task_ids: list[str | tuple[str, int]] = []
        end_date = execution_date if not future else None
        start_date = execution_date if not past else None
        locked_dag_run_ids: list[int] = []
        if group_id is not None:
            task_group_dict = dag.task_group.get_task_group_dict()
            task_group = task_group_dict.get(group_id)
            if task_group is None:
                return redirect_or_json(
                    origin, msg=f"TaskGroup {group_id} could not be found", status="error", status_code=404
                )
            task_ids = task_ids_or_regex = [t.task_id for t in task_group.iter_tasks()]
            
            
            dag_runs_query = select(DagRun.id).where(DagRun.dag_id == dag_id).with_for_update()
            if start_date is None and end_date is None:
                dag_runs_query = dag_runs_query.where(DagRun.execution_date == start_date)
            else:
                if start_date is not None:
                    dag_runs_query = dag_runs_query.where(DagRun.execution_date >= start_date)
                if end_date is not None:
                    dag_runs_query = dag_runs_query.where(DagRun.execution_date <= end_date)
            locked_dag_run_ids = session.scalars(dag_runs_query).all()
        elif task_id:
            if map_indexes is None:
                task_ids = [task_id]
            else:
                task_ids = [(task_id, map_index) for map_index in map_indexes]
            task_ids_or_regex = [task_id]
        dag = dag.partial_subset(