### 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)

nodes_dict: dict[str, Any] = {}
        edge_tuples: set[dict[str, str]] = set()
        for dag, dependencies in SerializedDagModel.get_dag_dependencies().items():
            dag_node_id = f"dag:{dag}"
            if dag_node_id not in nodes_dict:
                nodes_dict[dag_node_id] = node_dict(dag_node_id, dag, "dag")
            for dep in dependencies:
                if dep.node_id not in nodes_dict:
                    nodes_dict[dep.node_id] = node_dict(dep.node_id, dep.dependency_id, dep.dependency_type)
                edge_tuples.add((f"dag:{dep.source}", dep.node_id))
                edge_tuples.add((dep.node_id, f"dag:{dep.target}"))
        self.nodes = list(nodes_dict.values())
        self.edges = [{"u": u, "v": v} for u, v in edge_tuples]
def add_user_permissions_to_dag(sender, template, context, **extra):
    """
    Adds `.can_edit`, `.can_trigger`, and `.can_delete` properties to DAG based on current user's permissions.
    Located in `views.py` rather than the DAG model to keep permissions logic out of the Airflow core.
    """
    if "dag" not in context:
        return
    dag = context["dag"]
    can_create_dag_run = get_airflow_app().appbuilder.sm.has_access(
        permissions.ACTION_CAN_CREATE, permissions.RESOURCE_DAG_RUN
    )
    dag.can_edit = get_airflow_app().appbuilder.sm.can_edit_dag(dag.dag_id)
    dag.can_trigger = dag.can_edit and can_create_dag_run
    dag.can_delete = get_airflow_app().appbuilder.sm.can_delete_dag(dag.dag_id)
    context["dag"] = dag
before_render_template.connect(add_user_permissions_to_dag)