### 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)

select(TaskInstance.state, sqla.func.count(TaskInstance.dag_id))
            .where(TaskInstance.dag_id == dag_id)
            .group_by(TaskInstance.state)
        ).all()
        active_runs = models.DagRun.find(dag_id=dag_id, state=DagRunState.RUNNING, external_trigger=False)
        tags = session.scalars(select(models.DagTag).where(models.DagTag.dag_id == dag_id)).all()
        
        owner_links = session.execute(select(DagOwnerAttributes).filter_by(dag_id=dag_id)).all()
        attrs_to_avoid = [
            "schedule_datasets",
            "schedule_dataset_references",
            "task_outlet_dataset_references",
            "NUM_DAGS_PER_DAGRUN_QUERY",
            "serialized_dag",
            "tags",
            "default_view",
            "relative_fileloc",
            "dag_id",
            "description",
            "max_active_runs",
            "max_active_tasks",
            "schedule_interval",
            "owners",
            "dag_owner_links",
            "is_paused",
        ]
        attrs_to_avoid.extend(wwwutils.get_attr_renderer().keys())
        dag_model_attrs: list[tuple[str, Any]] = [
            (attr_name, attr)
            for attr_name, attr in (